Precalculus Course

Learn Precalculus in this full college course. These concepts are often used in programming.
This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check out her KZbin channel: / @lindagreen7859
⭐️ Lecture Notes ⭐️
🔗 Part 1 - Functions: lindagreen.web.unc.edu/files/2...
🔗 Part 2 - Trigonometry: lindagreen.web.unc.edu/files/2...
🔗 Part 3 - Conic Sections: lindagreen.web.unc.edu/files/2...
🔗 Part 4 - Parametric Equations, Polar Coordinates, and the Difference Quotient: lindagreen.web.unc.edu/files/2...
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Functions
⌨️ (0:12:06) Increasing and Decreasing Functions
⌨️ (0:17:35) Maximums and minimums on graphs
⌨️ (0:26:38) Even and Odd Functions
⌨️ (0:36:12) Toolkit Functions
⌨️ (0:43:18) Transformations of Functions
⌨️ (0:55:48) Piecewise Functions
⌨️ (1:00:19) Inverse Functions
⌨️ (1:14:34) Angles and Their Measures
⌨️ (1:22:47) Arclength and Areas of Sectors
⌨️ (1:28:39) Linear and Radial Speed
⌨️ (1:33:02) Right Angle Trigonometry
⌨️ (1:40:38) Sine and Cosine of Special Angles
⌨️ (1:48:41) Unit Circle Definition of Sine and Cosine
⌨️ (1:54:11) Properties of Trig Functions
⌨️ (1:04:50) Graphs of Sine and Cosine
⌨️ (2:11:23) Graphs of Sinusoidal Functions
⌨️ (2:21:36) Graphs of Tan, Sec, Cot, Csc
⌨️ (2:30:29) Graphs of Transformations of Tan, Sec, Cot, Csc
⌨️ (2:39:02) Inverse Trig Functions
⌨️ (2:48:49) Solving Basic Trig Equations
⌨️ (2:55:49) Solving Trig Equations that Require a Calculator
⌨️ (3:05:44) Trig Identities
⌨️ (3:13:16) Pythagorean Identities
⌨️ (3:18:37) Angle Sum and Difference Formulas
⌨️ (3:26:33) Proof of the Angle Sum Formulas
⌨️ (3:31:09) Double Angle Formulas
⌨️ (3:38:39) Half Angle Formulas
⌨️ (3:44:50) Solving Right Triangles
⌨️ (3:51:24) Law of Cosines
⌨️ (4:01:24) Law of Cosines - old version
⌨️ (4:09:44) Law of Sines
⌨️ (4:17:34) Parabolas - Vertex, Focus, Directrix
⌨️ (4:29:24) Ellipses
⌨️ (4:40:33) Hyperbolas
⌨️ (4:54:23) Polar Coordinates
⌨️ (5:01:55) Parametric Equations
⌨️ (5:13:22) Difference Quotient
--
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[@coldandafraid]

No one: KZbin at 3 am: "hey buddy, got 5 and a half hours to spare?"

[@NewsToday196]

There are 5 and a half hour if you aren't taking note if you are however it will at least 50+ hours

[@coldandafraid]

@@NewsToday196 indeed

[@Jaya-kq1ed]

@@NewsToday196 as this is basics it took me just 6-7 hours as I knew most of things from high school. Eb3n after taking notes.

[@amadiohfixed1300]

@@NewsToday196 not if you know a bunch of mnemonic techniques

[@fermiparadox6787]

@@NewsToday196 I went through the algebra course, and while taking notes it took about double the length of the video, 14 hours for a 7 hour video. the next step is practice problems which might fall into that 50 hours

[@Your_Boy_Suraj]

⌨️ (0:00:00) Functions ⌨️ (0:12:06) Increasing and Decreasing Functions ⌨️ (0:17:35) Maximums and minimums on graphs ⌨️ (0:26:38) Even and Odd Functions ⌨️ (0:36:12) Toolkit Functions ⌨️ (0:43:18) Transformations of Functions ⌨️ (0:55:48) Piecewise Functions ⌨️ (1:00:19) Inverse Functions ⌨️ (1:14:34) Angles and Their Measures ⌨️ (1:22:47) Arclength and Areas of Sectors ⌨️ (1:28:39) Linear and Radial Speed ⌨️ (1:33:02) Right Angle Trigonometry ⌨️ (1:40:38) Sine and Cosine of Special Angles ⌨️ (1:48:41) Unit Circle Definition of Sine and Cosine ⌨️ (1:54:11) Properties of Trig Functions ⌨️ (1:04:50) Graphs of Sine and Cosine ⌨️ (2:11:23) Graphs of Sinusoidal Functions ⌨️ (2:21:36) Graphs of Tan, Sec, Cot, Csc ⌨️ (2:30:29) Graphs of Transformations of Tan, Sec, Cot, Csc ⌨️ (2:39:02) Inverse Trig Functions ⌨️ (2:48:49) Solving Basic Trig Equations ⌨️ (2:55:49) Solving Trig Equations that Require a Calculator ⌨️ (3:05:44) Trig Identities ⌨️ (3:13:16) Pythagorean Identities ⌨️ (3:18:37) Angle Sum and Difference Formulas ⌨️ (3:26:33) Proof of the Angle Sum Formulas ⌨️ (3:31:09) Double Angle Formulas ⌨️ (3:38:39) Half Angle Formulas ⌨️ (3:44:50) Solving Right Triangles ⌨️ (3:51:24) Law of Cosines ⌨️ (4:01:24) Law of Cosines - old version ⌨️ (4:09:44) Law of Sines ⌨️ (4:17:34) Parabolas - Vertex, Focus, Directrix ⌨️ (4:29:24) Ellipses ⌨️ (4:40:33) Hyperbolas ⌨️ (4:54:23) Polar Coordinates ⌨️ (5:01:55) Parametric Equations ⌨️ (5:13:22) Difference Quotient

[@tonkotsu_noodles]

These comments should be pinned !!!

[@Your_Boy_Suraj]

@4th4rv alt lol😂

[@thenomad9963]

@@tonkotsu_noodles it's in the description so idk the point of this lol

[@tonkotsu_noodles]

@@thenomad9963 Oh yeah did n't see that when the author posted this Video. The author could have coppied from him ! lol... any way the point is this time stamp helps a lot !

[@thenomad9963]

@@tonkotsu_noodles true, true! well, i'm wrong, i guess this comment was useful after all! :)

[@slenderdluex3583]

🎯 Key Takeaways for quick navigation: 00:18 📊 A function relates input (usually x) to output (usually y), with each input having exactly one output. 02:34 🔄 Function notation (f(x)) represents the output value (y) when a value (x) is input into the function. 12:10 ↗️ A function is increasing if y values go up as x values increase; it's decreasing if y values go down as x values increase. 19:52 📉 Decreasing intervals: Describe where the function is decreasing in terms of x values. 22:44 📉 Local minima: Points where y values are lower than nearby values in an open interval around them. 24:39 🔁 Symmetry: A graph is symmetric with respect to the x-axis if (x, y) implies (x, -y) is on the graph. 27:41 ↔️ Symmetry: A graph is symmetric with respect to the y-axis if (x, y) implies (-x, y) is on the graph. 28:58 🔄 Graph is symmetric with respect to y-axis if (-x, y) is on the graph when (x, y) is. 29:26 🔄 Graph is symmetric with respect to origin if rotating it by 180 degrees makes it line up with itself. 32:33 🔄 Even functions: f(-x) = f(x) for all x. Odd functions: f(-x) = -f(x) for all x. 35:08 📈 Even function example: f(x) = x² + 3. Even both algebraically and symmetrically. 35:30 📉 Odd function example: f(x) = 5x - 1 / x. Odd both algebraically and symmetrically. 43:49 🔄 Transformations of functions: Outside changes affect y-values (vertical motions), inside changes affect x-values (horizontal motions). 50:24 🔄 Translations (adding/subtracting) affect y-values, horizontal shifts in opposite direction from sign. 54:35 📐 The rules for transformations of functions: Outside numbers affect vertical motions, inside numbers affect horizontal motions. Adding and subtracting correspond to shifts, multiplying and dividing correspond to stretches and shrinks. Negative sign corresponds to reflection. 55:48 📈 Piecewise functions are defined in pieces by different rules for different x values. Calculating values for piecewise functions involves applying the appropriate rule based on the given x. 59:21 🔀 Continuity of piecewise functions: Functions with transitions between different rules often have discontinuities at the transition points. 01:01:44 🔁 The graph of an inverse function is obtained by reflecting the graph of the original function over the line y = x. 01:05:37 🔄 Systematic method for finding inverses: Reverse roles of y and x, solve for y, and express the result as the inverse function. 01:07:24 ❌ Not all functions have inverses. A function must be one-to-one (satisfy horizontal line test) to have an inverse. 01:14:49 📐 Conversion between degrees, minutes, and seconds. 1 degree = 60 minutes, 1 minute = 60 seconds. 01:19:01 🔁 Conversion between decimal degrees and degrees, minutes, and seconds involves unit conversions based on ratios. 01:23:54 📐 Arc length is determined by the ratio of the angle to the total angle of the circle, multiplied by the circumference. 01:25:04 📐 Arc length formula: length = angle (in radians) × radius. Angle must be in radians. 01:27:28 📐 Area of sector formula: area = (angle / 2) × radius^2. Angle must be in radians. 01:29:12 📏 Linear speed = angular speed × radius for a rotating circle. 01:33:17 📐 Trig functions (sine, cosine, tangent) relate sides of a right triangle to its angles. 01:35:51 📐 Reciprocal trig functions (secant, cosecant, cotangent) are inverses of sine, cosine, tangent. 01:40:58 📐 Sine and cosine values for 30°, 45°, 60° angles: 1/2, √2/2, √3/2. 01:51:12 📐 The definitions of sine, cosine, and tangent are based on right triangle ratios: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent. 01:52:32 🌀 Unit circle definition: cosine(theta) is the x-coordinate, sine(theta) is the y-coordinate, and tangent(theta) is y-coordinate/x-coordinate of a point on the unit circle at angle theta. 01:54:22 🔄 Periodic property: Sine and cosine values repeat with a period of 2π (360 degrees), meaning sine(theta + 2π) = sine(theta) and cosine(theta + 2π) = cosine(theta). 01:55:43 📐 Pythagorean property: cosine(theta)^2 + sine(theta)^2 = 1, which originates from the Pythagorean Theorem applied to points on the unit circle. 02:02:18 🔎 Given sine(t) = -2/7 and t in quadrant III, cosine(t) is calculated as the negative square root of 45/7. 02:11:58 ⚙️ Shifting the graph: Adding or subtracting constants inside the function shifts the graph vertically. 02:17:30 📈 Understanding sinusoidal functions: Horizontal shifts, period adjustments, and amplitude changes in graphs of functions like y = a sin(bx - c) + d. 02:21:47 📉 Intuition for graphing tangent (tan) function: Relating slope of a line on the unit circle to the tangent graph, vertical asymptotes, undefined slopes, and periodicity of pi. 02:26:20 🔄 Graphing secant (sec) and cosecant (csc) functions: Converting from cosine and sine, vertical asymptotes, period, range, and domain. 02:37:57 🔄 Graphing transformations of tangent, secant, cotangent, and cosecant: Effects of amplitude changes, period adjustments, vertical and horizontal shifts. 02:39:11 ↩️ Understanding inverse trigonometric functions: Relationship between original trig functions and their inverses, domain and range restrictions, notation (arc, inverse), and graphical interpretation. 02:46:17 📐 The restricted domain of tangent (tan) function is from -π/2 to π/2, with vertical asymptotes at these endpoints. The range of restricted tan is from negative infinity to infinity. 02:48:41 🧪 Sine inverse (arc sine), cosine inverse (arc cosine), and tangent inverse (arc tangent) functions were introduced as inverse trig functions. 02:53:29 🕰️ Solving trig equations involves isolating the trig function, finding principal solutions in a given interval, then adding multiples of the function's period for all solutions. 03:07:49 ❌ Not all equations are identities. An equation that holds for some values of the variable is not an identity. 03:15:34 🔁 Pythagorean identity holds across different quadrants through symmetry. 03:41:22 📐 We derived the half angle formulas for cosine and sine: cos(θ/2) = ±√((cosθ + 1)/2) and sin(θ/2) = ±√((1 - cosθ)/2). 03:42:41 🔍 Given sine θ = 4/5 and θ in the second quadrant (π/2 to π), we found exact values: cos(θ/2) = 1/√5 and sin(θ/2) = 2/√5. 03:48:56 📏 Given one side and one angle in a right triangle, we used tangent to find the other side, and Pythagorean Theorem to find the hypotenuse. 03:51:11 📐 Solved triangles using side-side-side (SSS) and side-angle-side (SAS) using Law of Cosines and trigonometric functions. 04:05:20 📏 Applied Law of Cosines to find side length and angles in a triangle with known side lengths. 04:17:44 📐 Equations of a parabola: The equations y - k squared = 4px - h and x - h squared = 4py - k define parabolas. They're shifted by (h, k), and the distance |p| represents focus-vertex and vertex-directrix distances. 04:34:57 🥇 Ellipse equation and relationships: Ellipses elongated horizontally: x²/a² + y²/b² = 1. Relationship: a² = b² + c² (major, minor axis, focus-vertex distance). 04:37:12 📌 Equations for ellipses elongated vertically have x and y roles reversed, involving shifts in both directions. 04:37:41 🌟 Key points like vertices and foci can be labeled and calculated for ellipses with shifted centers. 04:39:24 🔵 The distance definition of a hyperbola involves the constant difference of distances to its foci. 04:42:12 🌀 Hyperbolas can have horizontal or vertical transverse axes, affecting their orientation like lying down or standing up. 04:43:34 📏 Hyperbolas' equations differ based on their orientation, involving parameters A, B, and C representing distances. 04:45:15 ⚙️ Formulas for distances to foci and vertices help derive hyperbolic equations, with A, B, and C being related quantities. 04:46:37 📊 Hyperbolas' slopes and equations of asymptotes depend on A and B, creating guidelines for drawing the curves. 04:49:27 ✒️ The conversion between polar and Cartesian coordinates involves trigonometric equations and understanding angles and radii. 05:00:16 🔄 Polar coordinates allow points to be represented with radius and angle, with adjustments for negative radii and angles. 05:02:27 📈 Parametric equations enable the description of curves using separate functions for x and y in terms of a third variable, often time. 05:02:54 📊 Parametric equations relate x and y to a third variable called the parameter, and graphing them involves finding corresponding x and y values for a given parameter value. 05:04:41 🔵 Graphs like circles on the xy-plane can be described by parametric equations (e.g., x = cos(t), y = sin(t)), and their Cartesian equation is often derived using trigonometric identities. 05:05:50 ⭕ Unit circles with radius 1 are described by x^2 + y^2 = 1 in Cartesian coordinates, and this equation can be parameterized using x = cos(t) and y = sin(t). 05:08:57 🔢 Parametric equations can also be created from given Cartesian equations, like parameterizing curves using x = t or other equations based on trigonometric functions. 05:11:07 📍 The equation of a circle centered at (h, k) with radius r is (x - h)^2 + (y - k)^2 = r^2, and parametric equations for circles are derived by scaling and shifting unit circle parametric equations. 05:12:49 ⚖️ Difference quotient and average rate of change concepts relate to the derivative and calculus, where average rate of change represents the slope of secant lines between two points on a function graph. Made with HARPA AI

[@kathrynmb]

This deserves way more likes, thank you 🎉

[@_PsyChoPaThiCX.___.]

Why this has only 5 likes. I got you bro

[@IcyLife3956]

Good comment 😁

[@corncobbob2326]

I saw this video on my feed and I want you to know that this is heavily appreciated. I hope whatever happens on your end, that things go well for you.

[@rahag-oz4dw]

thank you

[@luizhenriquebinharaarantes9901]

2020 conronavirus pandemic, day 240.: today i've decided to learn some calculus

[@Artyfficial]

17 year old me would be proud :')

[@debbiepolanco1527]

Me being in 8th grade and wanting to learn this so it would be easier in high school 👁👄👁

[@lacedemonio]

@@debbiepolanco1527 I'm 15 y/o, but in the next year's I'm going to go to the university.

[@debbiepolanco1527]

@@lacedemonio how??

[@zsalt2018]

@@debbiepolanco1527 similar situation, I’m feeling a little overconfident right now

[@josephwhite8992]

if you watch this and the 12 hour calc after it... your basically set for the semester. This stuff is gold!

[@iswear1667]

I didn't really study much precalculus when I was in grade 11. Since you have done it, I'm going to grade 12, will this be enough?

[@josephwhite8992]

@@iswear1667 absolutely, you should be fine, both videos cover basically everything you need to know

[@theunusual7631]

Can you give me the link for that video pls? That would be very helpful to me

[@jennifers6823]

where is the link for the 12 hour calc one? please?

[@josephwhite8992]

Sorry, my fault guys kzbin.info/www/bejne/fpekdKWBf8SMaNk

[@johnsmith2931]

Errors: 1. 1:24:47 10m should be 20m 2. 1:53:32 The answer to tan φ should be -2.7477 The answer shown was calculated by (cos φ) / (sin φ) when in fact tan φ should be calculated as (sin φ) / (cos φ) This is a great course and I am very thankful to have access to it for free. I am only listing these for the purpose of helping others, in case they were confused at these parts :)

[@estermusic3978]

2:32:48 what about shrinking the function by 1/pie?

[@user-fr1bm8bx3v]

@@estermusic3978 thx bro, I just got confused there for a day

[@hedgedoge5562]

Tysm I commented, and deleted it as soon as I saw ur comment

[@soulstealy781]

honestly 2 teacher errors for a whole 5 hour course ain't bad at all

[@randyevermore9323]

Another error: 2:05:31 -- The second-to-last column of the table shows t = 11π/12 but the notation for the circle shows t = 11π/6. The latter is likely correct.

[@ErikMrazBR]

After some days watching 30 minutes per day I finished this course and i'm going to calculus 1 course. Thank you for this incredible job, Dr. Linda

[@ErikMrazBR]

@Android Investment I decide what is supposed to be enough, lol. I already done all my math courses in college. I just like to re-learn everything again.

[@Unkown242]

@MasterCourse TV I am doing 9 hours each day, its the third day at 1hr 46 min, also taking notes

[@SoulOne713]

@MasterCourse TV L I F E

[@mauriciocastroguillermo9287]

@@ErikMrazBR Hi, could you say this is the most complete precalculus course on KZbin?

[@ErikMrazBR]

@@mauriciocastroguillermo9287 I'm not inside other youtube precalculus courses. What I can say is that is pretty good course and it can help you.

[@aidenramirez5126]

For anyone else using this, at 1:25:09 the arclength should be 20m instead of 10m. Otherwise the video is tremendously useful, thank you for your work!!!

[@SmokeyCherry467]

Bruh facts bruh, bruh thanks bruh

[@halifanaccount2216]

B)

[@DespianJosh]

@@SmokeyCherry467 bruh

[@NG-ug6bv]

bruh no lie bruh i was stuck bruh thx bruh

[@johnx140]

@@NG-ug6bv damn bruh that sucks bruh hope youre good now bruh

[@ltcolumbo1717]

Great refresher before taking college calc finished in about a week, would recommend for any person to take the summer before they start a STEM major in college. Next up the calculus courses :)

[@user-th7cu9ll4j]

i am exactly in your position ahaha as an incoming freshman student.

[@fermiparadox6787]

@@user-th7cu9ll4j I'm sorta in your position, realized online classes left me woefully unprepared for my 10 week summer calc 2 course, now im back here relearning it all

[@lolmanittakesguts]

@@fermiparadox6787 best of luck in calc 2 dude you got this

[@fermiparadox6787]

@@lolmanittakesguts thanks man

[@ih2246]

@@fermiparadox6787 I’m in your exact situation

[@miriosdick5682]

I just wanted to say, thank you so much for this free course and I'm really grateful for all the work you put in these videos. I'm 16 years old and my school system sucks, our math is really bad and without you I don't know if I was going to continue learning math aside from the stupid school system that doesn't help at all. Books are also a great source of information, I'm very thankful that people like you exist.

[@c.g.7144]

Hey there, I just wanted to say good job. I'm super impressed you are taking the initiative and finding other ways to learn yourself. Im sorry the school system is failing you. Keep going. Keep searching and learning and researching yourself. You are going to do awesome in life.

[@supershaw3651]

You my friend, hey you up above, You are not alone. We have terrible teachers especially with math snd english, bad guidance counselors, people who don't give two rips, and A very bad ACT Average. A freaking 17 after taking it two times. I'm currently a senior and have a 29 somehow. I scored better than like 98% of my class which is shocking. I've had dang enough of it so I'm currently learning some Actual math for once because Our teachers can't do crap.

[@humblejo130]

I'm sorry to hear that man. Go ahead and get it while you can

[@spooneytoon7407]

Likewise bro shows something big in you I’ve taken the initiative of educating myself in prep for college cause our school is crap

[@maylin1986]

Thank you for such a comment and doing everything you can to take the initiative. I also had a hard time with school, but mostly math was the worst subject for me. I hate that the education system is only getting worse and for sure failing you. I use to hear of life skill classes being taught when my parents went to school and prior. Now, schools in my generation are removing recess and Art, Music or certain sports due to lack of funding. It's just a shame that todays schooling sytems are cheating you out of a good start into the world, but I'm glad you're all standing up for yourselves to get that kick-start into the world on better footing and have the free tools online to do so. 💛

[@jameswoodford282]

Watches on 2x speed to be confused twice as fast😎

[@GruppeSechs2004]

So, if I play it at half-speed, I’ll only be half as confused? 🤔

[@zayanismath9292]

@@GruppeSechs2004 we're making progress people less goo

[@kavinnath1504]

@@GruppeSechs2004 No, you'd be fully confused but at half the speed.

[@pauladen3037]

🤣🤣

[@aliabassi8045]

​@@GruppeSechs2004Wait so if I play it at 0x speed, I won't be confused??? 😳

[@dulxbe4883]

took me a month, but I finally finished the video :))

[@wolfgod1664]

Taking summer pre call at college. I’m expecting this.

[@adhishnanda]

Lol! But at least you finished it. Kudos to you!!!!

[@enolaholmes3489]

Is this a good video ??

[@dulxbe4883]

@@enolaholmes3489 it was a good refresher course before I took calc I

[@Gabriel-dr9ru]

Where does the 6a in the 3:25 come from?

[@michaeldavis2906]

I’m 25 years old, have a full time job and not even in college, yet decided that I want to learn some math today! I’m only 7 minutes in and I got to say that the way the teacher is teaching this course is very relaxing and soothing!

[@frankieramos8017]

What do you do man if you don't mind me asking?

[@gamergenix893]

@@frankieramos8017it’s been a year did you find out?

[@zion101ification]

You guys are really doing a awesome job to make this courses accessible to others for free, this is the best thing anyone can do for the whole mankind

[@amaan999]

IS THIS VIDEO IS HELPFUL FOR PRECALCULUS BEGINNERS ALSO??

[@JM-iv5rk]

@@amaan999 yeah. I wish I watched this video before taking pre-cal last semester 😩

[@daughteroftheking3220]

Right I wish I knew this resource existed when I was in high school. Right now I’m in college and math isn’t even my degree but I just think it is important to learn and refreshen my mind.

[@justanorthernlight]

Thank you for this class, I've watched a lot of youtube videos on the subject but this is the first time I've felt like I really understand the non-triangle parts of Trigonometry.

[@gdahlm]

I really do appreciate this video for my review after decades. That said there is an error at 1:25:10 2.5 * 8 is not 10, it is 20. It would be nice if there was an annotation added to call that out.

[@jackychan8539]

Thank god

[@reginaldmalloy7923]

OMG I thought I was losing my mind lol

[@NaveenKumar-wn7op]

@@reginaldmalloy7923 same

[@DroughtBee]

Thank you about to have a stroke thinking my whole basis of foundations of mathematics is false.

[@readtolead1531]

This is so satisfying and comfortable We want more courses like these

[@ADA98310]

No Joke this is one of the best teachers i have ever seen. She explains to you things in a away that refreshes your memory and makes things that didn't make sense before finally make sense. probably because we got taught poorly. This is truly a gift. Thank you!!!

[@steffc6914]

This is amazing. You have no idea how grateful I am for this. Thank you. Thank you Dr. Green

[@0berke1]

just finished and I'm so thankful. The basic explanation of each idea was really helpful. cannot wait to start the calculus 1 course.

[@elizabethmonk2205]

Thank you for this course. The last math class I had taken was honors pre calc (college credit) in my junior year of high school. Trying to review topics before taking business calc in winter quarter.

[@deenrqqwe6794]

I'm halfway through and I am grateful for this course!

[@OhmVibe]

About half way through this course and just wanted to express my gratitude for all these lessons. I started with the College Algebra video a few months ago, and now I'm here. I never thought it was possible to learn math this quickly!

[@wonsoongi749]

i took a gap year to study for my uni entrance exams and i watch these videos almost daily, as well as some of the programming tutorials, and it's like i've signed up for an amazing college boot camp for free! i truly appreciate the effort that goes into producing these videos

[@roycec5843]

How’s it going now? In Uni yet?

[@wonsoongi749]

@@roycec5843 yes! in uni for compsci now

[@thelegendaryskits820]

@@wonsoongi749hi, how is it going so far? I am in 12th grade and i have really set my mind on doing compsci for my cc and uni years at first i was a little on the edge of compsci and software engineering but i think i will do comp sci, do you have any tips or anytbing that can help out? Thank you

[@virgil_anxiety770]

i get to learn advance stuff i'll need for my major, thank you so much. You guys are life savers. Please don't go anywhere! I'm gonna have these videos with me through the whole summer

[@lilimonarch8494]

I haven't even watched the video yet but my appreciation is so huge. My teacher was gone for 2 months so we missed out on a lot of stuff. Feeling the gap right now but thanks to you, catching up will be so much easier

[@rickennmakesgames]

going to be putting this on while i sleep

[@zigginzag584]

Yeah, if that worked, I wouldn't be here 15 years after high school trying to learn this stuff.

[@Wrathos]

@@zigginzag584 Haha dont worry mate. You didn't need it in high school, now you do. Now its the time to learn it. You got this. Keep at it brother

[@Kazekoge101]

Tyler Prometheus it wasn’t interesting in high school in the mid 2000s though, or taught interestingly tbm specific

[@alfredhitchcock45]

haha

[@harshbarj]

Well, it will put you to sleep. That's for sure! 5 min in and I'm already glazing over.

[@alphabet9182]

This course is amazing and free! Subscribed without hesitation!

[@dhaloh]

I'm so thankful for this course being shared free. I didn't understand maths as a kid and missed out on a lot in high school. It's been 3 years since I graduated and I want to study Computer Science in uni but don't want to be an absolute 0. This course helps a ton.

[@smoothstriker7475]

Finally finished in 10 days with notes!!! Thank you for this video! I will be watching Calc next you are amazing professor Linda!!

[@_quixote]

10 days??

[@yook1358]

@@_quixoteyou would have to watch 3-4 parts of this everyday to finish this course in 10 days

[@srivishnubobde4858]

@@yook1358 ya, so, its not much!!

[@misuzu1flv629]

i found this channel like a minute ago when this was posted wow

[@cartoons__for__kids_Hindi]

You just found heaven

[@1CT1]

Who hath ears to hear, let him hear.[Matthew 13:9-16 KJV] I come with a message to tell everyone that even though times are hard, and it seems endless as though at times it never shall pass, these like other things shall pass and these to shall come to pass, and a new beginning shall arise for you. May God bless anyone who is is in need or is in turmoil in the blood of Jesus Christ our Lord and Savior, and king of kings, and Lord of Lords amen right now, for God is a merciful God. Call on God and he will not be deaf but God will listen for he loves you no matter the circumstance for we are all his children from those whom accept his son Jesus Christ and the gift of salvation bestowed upon us by God through the vessel and blood bought sacrifice of him Christ Jesus whom he the father almighty God hath sent in him Christ Jesus in that of his and our fathers name, know to this even if you doubt it or are uncertain or even yet too feel unworthy at times due to what had happened or the events in your life for it is written! He will not abandoned those in distress but bless the ones who mourn! Accept God and Gods son Jesus Christ our Lord and our Savior, and king of kings, and Lord of Lords and you shall receive the gift of eternal life and be renewed with that of the abundance in that of the Holy Spirit now and forevermore! Have a wonderful day/night everybody, and farewell!(Share the message around the world!)

[@battlebuddy4517]

Ellis Terrell stfu

[@zigginzag584]

is this some fancy new way of saying "first"?

[@rubenalejandro7763]

this is probably the best single free resource available for learning code

[@bigmike69]

I have a precalc final in about 12 hours this is gonna be so helpful!

[@centauria9122]

Did ya pass? I'm going to tale pre-calc sometime towards the end of next year, along with inorganic chemistry, and some other class.

[@aname7862]

Same 😅

[@Iinustechtips]

@@centauria9122 its hard you need to practice. practice is really important!

[@Obito_17-52]

@@Iinustechtipsis precalc hard ?

[@Iinustechtips]

im in calc ab/bc now. it is super important to get your pre calc down. it was hard, but looking back, its nothing compared to calc ab and bc@@Obito_17-52

[@user-qv3bu8ud9o]

At 1:31:00 unit can be radians / seconds(as it's the SI unit), so if it's in seconds then u gotta divide 2pi by 120 (converted to sec from 2 mins) which will equal one-sixtyeth of pi. If u multiply that with 20 u get one-third of pi which is the linear speed in units of meters/seconds(again SI units).

[@BoZhaoengineering]

Your video is very cool. Never thought pre calculus is taught in a such efficient way!

[@DoggletPug]

This channel is awesome! Thank you guys so much for bringing knowledge to the world! During quarantine, it's harder than ever for people who want to get ahead, to stay ahead, and with you guys preparing us for the world, There's no telling what we can do! I wish I had discovered this channel earlier, you guys rock!

[@georgesadler7830]

Thank you so much for an outstanding video/lecture on Precalculus. Every major topic is covered in precalculus. These topics will only help students moving on to Calculus one and beyond.

[@ROZAY305BOSS]

Amazing video! I am a long time high school graduate returning to engineering school and this video is extremely helpful in regaining my hold on math.

[@TheFoooL]

Thank you so much especially for the part of graphs of sinosudial functions at 2:11:23 I was struggling with it as my teacher struggled to explain it

[@osamadias1756]

Thanks for this video it's amazing and clear. For once I understand what's going on in precalc and the teachers in this video don't bring expressions or numbers from outer space neither do they skip saying what they did in any step. I believe the teachers in this video are intelligently smart and credible. 😍😍😍😍😍😍😘😘❤❤😊😁👍

[@tinam6712]

THANK YOU SO MUCH DR. LINDA GREEN! This is extremely wonderful :))

[@arisfionna239]

thank you free code camp for making education easy to reach, education is so important and you guys do an amazing job with all your courses!!

[@kornelsylwester]

Can you make a course about electronics? Thank you for all the amazing videos you've been putting out!

[@shubido8980]

I'm starting university in a few DAYS this would be one of my life saving videos!!! Thank you!!!

[@user-mz2vz8ok3x]

Hi how is uni by now?

[@__Hanasei__Levinus__]

Ye how is uni OP?

[@elenabermejo1732]

Thank you so much for all your work. I want to go back to school for engineering but before I can do that I have to save money to go back to school. In the mean time I will brush up on my math so Im ready when ai jump back in. You deserve the world ❤️

[@foxpaw5797]

Thank you so much for the free course. I can’t take pre calc through my school because of my schedule and I needed this 🥰🥰

[@nitie6042]

Like it's way of clearing concept easily.👍🙏

[@subhashkumar6406]

1:17:40 when u feel sleepy in class i enjoyed the class though.

[@mohamedghacham7676]

lmaooooo

[@yesnt8907]

😂

[@marcoeibrink4639]

Thought i was tripping

[@someonesomeone3126]

Lol i thought i was hallucinating

[@hughjanus7176]

A wonderful video for revision, finished in 3 hrs. Thankyou Professor

[@janicesmyth2183]

Thank you so much Dr Green! I wish I had a teacher like you when I was a girl! My grandkids are benefiting from your generousity! God bless!

[@Lorena-mh5zd]

Amazing how I can learn more in 5 hours than in the entire school year

[@ninadee9753]

Imma do this in the summer to prepare for precalc. Thank you for this video!

[@blandface9957]

I'm in the same boat lol

[@aliciavaldez3032]

Me rn currently AHHH I’m taking pre calc for my senior year gotta be prepared AHHHH

[@ninadee9753]

@@aliciavaldez3032 You got this!!

[@luxeave]

very grateful for this course, hopefully next is calculus, already one foot in DL & RL without solid mathematical background

[@Gunta87]

This video really helped me to prepare for first semester of college!

[@anujyadav7428]

Make a course on discrete mathematics.

[@bushraashkir635]

YES PLEASE!!!!!!!!!!!!!!!!!!!

[@theodorosmavoglou9653]

what do we call "discrete mathematics" ?

[@benv4514]

@@theodorosmavoglou9653 if they told u it wouldnt be so discreet

[@theodorosmavoglou9653]

@@benv4514 🥲

[@canilo_7672]

@@theodorosmavoglou9653 computer science math type of thing

[@satyaaravindpandavula4832]

This is a whole semester in 5 hours!!🔥

[@lijizhen3326]

For university?

[@mtutoriales]

Not true. It was mostly trigonometry, the video didn't even cover limits.

[@justaguy1951]

@@mtutoriales isn't precalc just a bunch of trig and some calc to prepare you for an actual calc class?

[@beri4138]

@@lijizhen3326 This is high school level. Calculus 1,2 and 3 are the university courses.

[@kermitthefrog5028]

@@beri4138 some high-schools you can take calc 1

[@blxeberry0]

Thank you so much dr. Green! I think I can speak for most students when I say free education at this quality is like gold. None of this would be possible without you, so tysm❤!

[@PlumOps]

This can't get better than this ! Brilliant !

[@jirisykora9926]

Great! Please more videos like this! I really hope for that, because when I go to University, I need to know this, not only computer science and coding.

[@jakehardy5997]

Don’t forget calculus as well 🙃

[@azhisazhis6931]

Hey i wanna ask, should i learn some basic math highschool before learn this?

[@yamatanoorochi3149]

​@@azhisazhis6931this is basic high school math

[@yamatanoorochi3149]

Oh comment is a year old already

[@Carrbonara586]

My entire year of learning Pre-Cal in just 5 hours....... what have I done with my time???? :v

[@battlebuddy4517]

Ellis Terrell stfu

[@__________6931]

@@battlebuddy4517 😂

[@Red-yq6nc]

@@1CT1 STFU

[@HVNDAL]

@@1CT1 BASED

[@oro-oluwatoromo-thewordoft7339]

Ellis Terrell thank you so much

[@hugegaylover0029]

oh my gosh, thank you for this! now i can start understanding university maths with this information! i cannot thank you more!

[@love-gn5zt]

I just started taking this in highschool and they gave me this class this year as a junior

[@zeyadhany5122]

I hope they upload a course in calculus 3. This would be really helpful.

[@seamus4A]

I agree 100%

[@deicidej89]

Thanks for this: ⭐️ Course Contents ⭐️ ⌨️ ( 0:00:00 ) Functions ⌨️ ( 0:12:06 ) Increasing and Decreasing Functions ⌨️ ( 0:17:35 ) Maximums and minimums on graphs ⌨️ ( 0:26:38 ) Even and Odd Functions ⌨️ ( 0:36:12 ) Toolkit Functions ⌨️ ( 0:43:18 ) Transformations of Functions ⌨️ ( 0:55:48 ) Piecewise Functions ⌨️ ( 1:00:19 ) Inverse Functions ⌨️ ( 1:14:34 ) Angles and Their Measures ⌨️ ( 1:22:47 ) Arclength and Areas of Sectors ⌨️ ( 1:28:39 ) Linear and Radial Speed ⌨️ ( 1:33:02 ) Right Angle Trigonometry ⌨️ ( 1:40:38 ) Sine and Cosine of Special Angles ⌨️ ( 1:48:41 ) Unit Circle Definition of Sine and Cosine ⌨️ ( 1:54:11 ) Properties of Trig Functions ⌨️ ( 1:04:50 ) Graphs of Sine and Cosine ⌨️ ( 2:11:23 ) Graphs of Sinusoidal Functions ⌨️ ( 2:21:36 ) Graphs of Tan, Sec, Cot, Csc ⌨️ ( 2:30:29 ) Graphs of Transformations of Tan, Sec, Cot, Csc ⌨️ ( 2:39:02 ) Inverse Trig Functions ⌨️ ( 2:48:49 ) Solving Basic Trig Equations ⌨️ ( 2:55:49 ) Solving Trig Equations that Require a Calculator ⌨️ ( 3:05:44 ) Trig Identities ⌨️ ( 3:13:16 ) Pythagorean Identities ⌨️ ( 3:18:37 ) Angle Sum and Difference Formulas ⌨️ ( 3:26:33 ) Proof of the Angle Sum Formulas ⌨️ ( 3:31:09 ) Double Angle Formulas ⌨️ ( 3:38:39 ) Half Angle Formulas ⌨️ ( 3:44:50 ) Solving Right Triangles ⌨️ ( 3:51:24 ) Law of Cosines ⌨️ ( 4:01:24 ) Law of Cosines - old version ⌨️ ( 4:09:44 ) Law of Sines ⌨️ ( 4:17:34 ) Parabolas - Vertex, Focus, Directrix ⌨️ ( 4:29:24 ) Ellipses ⌨️ ( 4:40:33 ) Hyperbolas ⌨️ ( 4:54:23 ) Polar Coordinates ⌨️ ( 5:01:55 ) Parametric Equations ⌨️ ( 5:13:22 ) Difference Quotient

[@thatonecommentor7758]

Thank you!!

[@fireemblem2770]

The precalculus course I wanted and needed but never got... until now!!

[@cerenkarahan5838]

I just finished this. I am proud of myself even tho I am confused. I will keep working hard :)

[@Ivy-hg8us]

This is really useful! I was in 7th grade and self studied the AP Pre-Calculus exam. Thanks to this, I got a 5 in my exam.

[@user-kf8ek7bi4p]

The AP precalculus class or test still didn't start yet? The first AP precalculus test is in May 2024...

[@melc-centex1091]

I so appreciate this free course for a refresher!!!

[@mikel4662]

Yes I agree.

[@kaungphyowai5261]

Thanks

[@koichitoyama6859]

Just the thing I needed! Thanks a lot!

[@andybanda2366]

I'm a junior in high school some of the subjects she touched on I learned the year before in algebra2 but other than that very helpful since I was a bit lost in a class full of seniors who also didn't know much it helped me a ton ( I swear I am not a nerd or geek)

[@yang_er]

Thank you so much for this video. I am speed-running college Maths before my freshman year in August. I learned a lot from this video. Took me 3 days to finish the whole thing (also included some practice). Best channel on KZbin 🫶🏻

[@beatrizeugeniagrisalescast4236]

I LOVE THIS CHANNEL!

[@bassome3000ify]

Freecorecamp, i fricking love ur efforts

[@sachinipoornima3482]

Done. This is the second mathematics video that I have watched. Thank you very much

[@denzeltownsel5410]

Thank You Dr. Linda Green.

[@rfqa4116]

I'm a first year mechanical engineering student and recently dropped calc 1 before i could fail it. Ive never been particularly good in math (ironic ik considering i went into one of the most math heavy majors there is lmao). I have some serious holes in my math knowledge due to my long history of being a lazy student. Im deciding to take this couse before moving on to calc 1. Really hope i can finally stop considering myself to be bad at math after this!!

[@EragonShadeslayer]

Yes this is a good approach, with math you really need to know the previous stuff before you can advance so make sure you know all the previous things

[@jairabelleventurillo7480]

Please do physics . Can't wait. Thank you so much

[@yoismak]

Thankyou soo much!!! I was looking for a course for pre calculus!

[@zion101ification]

I refrain from posting comments online but for this channel it’s worth it👍.. Lots of courses thanks guys 🤝

[@guymanson1626]

This video was extremely helpful. I used to toss and turn at night kept awake by my ADHD, but after playing this and lying in bed, I slept like a log

[@jacobaferman]

I really like how at 1:17:40 she ascended reality

[@ramonehenry8491]

Thank you so much for this!!

[@jiminnoodlesoupwithasugaon1915]

using this as a refresher while studying comp programming hits different

[@utena8518]

Omg yes! Please tell me next is going to be calculus, after 1 month I have an exam in calculus 2 D:

[@1CT1]

Who hath ears to hear, let him hear.[Matthew 13:9-16 KJV] I come with a message to tell everyone that even though times are hard, and it seems endless as though at times it never shall pass, these like other things shall pass and these to shall come to pass, and a new beginning shall arise for you. May God bless anyone who is is in need or is in turmoil in the blood of Jesus Christ our Lord and Savior, and king of kings, and Lord of Lords amen right now, for God is a merciful God. Call on God and he will not be deaf but God will listen for he loves you no matter the circumstance for we are all his children from those whom accept his son Jesus Christ and the gift of salvation bestowed upon us by God through the vessel and blood bought sacrifice of him Christ Jesus whom he the father almighty God hath sent in him Christ Jesus in that of his and our fathers name, know to this even if you doubt it or are uncertain or even yet too feel unworthy at times due to what had happened or the events in your life for it is written! He will not abandoned those in distress but bless the ones who mourn! Accept God and Gods son Jesus Christ our Lord and our Savior, and king of kings, and Lord of Lords and you shall receive the gift of eternal life and be renewed with that of the abundance in that of the Holy Spirit now and forevermore! Have a wonderful day/night everybody, and farewell!(Share the message around the world!)

[@battlebuddy4517]

Ellis Terrell just stop trolling

[@bobhrobor4654]

It was before on this channel

[@dmitryiy.4405]

@GabzBoni I have searched the website and couldn't find a link to their Calculus course. Can you provide a link please?

[@GhostinTube]

@@1CT1 but does jesus know calculus though?

[@DrLouellLSala]

wow. this is great and very helpful

[@1CT1]

Who hath ears to hear, let him hear.[Matthew 13:9-16 KJV] I come with a message to tell everyone that even though times are hard, and it seems endless as though at times it never shall pass, these like other things shall pass and these to shall come to pass, and a new beginning shall arise for you. May God bless anyone who is is in need or is in turmoil in the blood of Jesus Christ our Lord and Savior, and king of kings, and Lord of Lords amen right now, for God is a merciful God. Call on God and he will not be deaf but God will listen for he loves you no matter the circumstance for we are all his children from those whom accept his son Jesus Christ and the gift of salvation bestowed upon us by God through the vessel and blood bought sacrifice of him Christ Jesus whom he the father almighty God hath sent in him Christ Jesus in that of his and our fathers name, know to this even if you doubt it or are uncertain or even yet too feel unworthy at times due to what had happened or the events in your life for it is written! He will not abandoned those in distress but bless the ones who mourn! Accept God and Gods son Jesus Christ our Lord and our Savior, and king of kings, and Lord of Lords and you shall receive the gift of eternal life and be renewed with that of the abundance in that of the Holy Spirit now and forevermore! Have a wonderful day/night everybody, and farewell!(Share the message around the world!)

[@battlebuddy4517]

Ellis Terrell stfu

[@martinamarino4786]

everything is so nicely explained and clear

[@anotherway1777]

Well that’s nice. I’m going to brush up on Precal and Single Variable before I go back to school to take Calculus 3. Thanks!

[@bikdigdaddy]

*I just begged for this course in the last video and here it is.* *Thanks FreeCodeCamp* ♥️

[@abaundwal]

Lol yeah. Surely their only motivation behind creating this course was that Panda Editz ツ ... THE Panda Editz ツ himself ... asked them to make it. >:)

[@bikdigdaddy]

@@abaundwal :D you made me valuable 😂

[@rainerrilke5093]

@@abaundwal x)

[@idiotsincarsalberta]

now that I'm almost done Calc II, it's crazy how easy this stuff is, even though I only took it in high school just over a year ago.

[@scarlol1800]

must be nice😊

[@_quixote]

i feel disappointed in myself because i'll probably struggle with this

[@highviewbarbell]

@@_quixote im in college algebra right now and this stuff seems impossible, but in a year it'll be easy and in three I'll be doing Analysis, so don't worry about that stuff at first. Just take everything a step at a time and keep improving.

[@lanceearvin]

Just finished the course. Thank you so much for this very helpful content!!!!

[@PAshish-dh5fk]

I cant download the notes ... Did you?

[@captainnemo3123]

Thanks it helped me revise precalc.

[@LeoDaSoR]

there's a mistake in 1:24:48 it should be 20 not 10

[@kukluxklangaming2060]

Same thanks bro

[@betterbutter5935]

@@dcpark0509 me 2 ahahahha

[@FaiGal]

Please do a Calculus 1 course for another video. I need to refresh before taking Calc 2 this semester

[@user-qy6tu9ip9v]

Do you need to memorize the unit circle to do well in calculus? Please help.

[@sanamRajan]

wow thats awesome please we need such a videos about advanced calculus for programmers

[@Barri1]

My Journey 29/05/2022 DAY #1: 3:13:50 (Skipped to 1:14:55, already seen on the Algebra Course. And skipped "Linear and Radial Speed", "Graphs of Sinusoidial Functions", "Graphs of Sec, Cot, Csc" and "Inverse Trig Functions") DAY #2: 4:17:43 DAY #3: DONE! Took 2 weeks 13/06/2022

[@icy89]

I took calculus 1 and struggled so badly (my math skills aren't that strong) so here I am trying to get through this video and the calculus 1 video before I take calculus 2 this semester-

[@makeki7756]

same bruther

[@ammaramy5438]

Dud frist i think that u have to take algebra full course to understand this calculus stuff

[@ammaramy5438]

By the way now i am here because of that i finished the college algebra full course from this channel and now am her to learn calculus coz of that i need them for my grade 12 national exam 😉😃

[@icy89]

@@ammaramy5438 yeah... this summer I'm gonna spend a lot of time reviewing algebra because turns out I understand the concepts in calculus 2, but man I am REALLY bad at algebra so I've been doing poorly again LOL. Oh well... I only got calculus 3 left and after that I NEVER have to see calculus again 🤡

[@muhammadharoon2304]

Make an courses on chemistry and physics too!

[@nuebayown6589]

Chemistry and Physics for Engineering ! Yes !

[@w.schumann4372]

Those are some very broad topics. If you're looking for Chemistry videos, Organic Chemistry Tutor is a great source of information on organic and inorganic chemistry! He posts Physics and Math videos as well, with some playlists spanning 300+ videos

[@joeyGalileoHotto]

The Organic Chemistry Tutor has full length course videos on Chemistry and Physics that would be given to students as a introduction and/or review for a final examination.

[@sida_g567]

We need physics for game engine not chemistry

[@dusscode]

Sid 23x who said anything about a game engine?

[@user-qe2nx9nw7h]

the best videos i've ever seen i'm watching from algebra and its the second video which i finished although there r things which repeated but every time you watch u get something new

[@dernayt2728]

Usefull video to refresh my maths before starting college

[@tofan505]

yes PLZ can we get more math and C

[@OAdnanGonzaga]

1:53:32 there is a error here tangent is 0.9397 / -0.3420 = -2.7476... the result on the video is -0.3639

[@jethroegatbunton2983]

yes I saw that as well

[@karrielau4227]

thanks! I was so confused about that part!