Introduction to Trigonometry: Angles and Radians

[@pinklady7184]

After years of learning mathematics, I didn't really know what a radian was. Thank you for explaining it.

[@gideonjake6475]

Instablaster...

[@nickmcguirk5993]

Same here! My wife, who teaches geometry and knows I’m somewhat good at math ☺️ was shocked. Our relationship may now crumble 😅 but yeah now for work I am learning about water velocity and flow, and was stumped by a question of calculating the area of a segment…. Two days later I’m only a lifetime away from being a master. 👍👍

[@amiyakumarchowdhury5283]

Hows it going now?​@@nickmcguirk5993

[@ontan7287]

I've been struggling with trig for months because of these topics the video has mentioned. It's explained with a lot of clarity. My teacher goes too fast so I wasn't able to grasp this until now. Thank you so much Professor Dave.

[@freudsghost]

I have pretty bad dyscalculia (math dyslexia) and even though I have always been able to complete/pass math classes, and get through college courses, complete a degree in and now work in STEM (electrical & computer engineering/physics) - sometimes I still struggle to remember the basics correctly and things get jumbled up in my dyscalculic brain. I really love math and physics so when I need a refresher course on trig - diffeq I come back to Professor Dave's videos. Dave is a fantastic teacher (he explains clearly, slowly and in-depth with direction) and I appreciate that I can pause and rewind and have a constant visual of what he's talking about! Really helpful for anyone with learning disabilities! I would recommend these videos to anyone who wants to learn these subjects for the first time or is struggling in their school courses and needs supplementary tutoring as well!

[@guacre2675]

That's honestly kind of encouraging to read. I want to go to college for mechanical engineering, but I always forget how to do simple operations like factoring correctly.

[@lauramoreno8742]

His vids are the best and most uncomplicated on KZbin

[@kaiserquasar3178]

ikr never understood trig until now

[@trooperzooper6092]

Basically whoever is getting confused in last question with 600°, Subtract 360 ° from 600° . If you're unsure about an angle like 600 degrees, remember that angles repeat every 360 degrees. Subtracting 360 from 600 gives us 240 degrees, which is the equivalent angle within one full rotation. Converting 240 degrees to radians results in 4/3π. 240/180 is simplified to 4/3.

[@kevinlehde2650]

I love your videos - clear, concise, easy to understand. I assign them to my students as a supplement in case they need it. I would nitpick one thing: the very first image shows two rays and calls them "coterminal". But they are not coterminal, because they would be on top of each other. They do start from the same point, but that doesn't make them coterminal. I wouldn't bother mentioning it, but I notice a lot of comments below about whether we can say that two angles are "equal", like pi/2 and 5pi/2. What I would say is that these angles are coterminal - that is, they both end in the same location as you go around the circle. So I would save that word for that use instead. I really am a fan, I hope this doesn't come off as pedantic. Your takedowns of flat earthers are epic.

[@LeBron652]

the best of radian explaining, thank you

[@KyleGustinSEO]

If only I had found this short video sooner. So much confusion would have been avoided! Thank you!

[@ElPurroco]

You are the most brilliant teacher I ever met ...

[@georgesadler7830]

Professor Dave, thank you for a fantastic Introduction to Trigonometry: Angles and Radians.

[@craigasauruswrecks4915]

Hey! Just noticed at 5:43 The answer for 600 Degrees is inaccurate, taking (600/180) is 3.33repeating. This would give us a fraction of 10(pi)/3 not 4pi/3

[@fahadshaikh5686]

Same bro stuck on this for 10 min 😅 and even doubted my whole journey through playlist till now 😂

[@craigasauruswrecks4915]

@fahadshaikh5686 sometimes I think they leave errors in to see if people are really learning! Or they're human and make mistakes like the rest of us

[@shaandutta3541]

600 degrees is 2 revolutions (720) minus 120 thus we end up in -240 giving us 4 pi/3

[@LEBIC_official]

​@@shaandutta3541so we write where we reach or we write how many revolution it makes ?

[@LEBIC_official]

​​@@shaandutta3541 720 degree is 4 pi and 120 is 2pi/3, so if we subtraction we get 10 pi/3 And not only this I did the other way too 360 is 2 pi and 240 is 4pi/3 if we add this both by taking the LCM we will get 10pi/3 Idk but i think 4pi/3 is wrong Please correct me if I am wrong

[@nimaemami6709]

Thank u sooo much! I am soo excited to start trigonometry!!!

[@mercybitrus6914]

God bless you prof Dave

[@Sandeepboi]

A great lesson with simple tutorial. I am loving it.

[@titanrayven3275]

Hi Prof Dave! Would it be okay if I link your videos to my learning modules that I created in Canvas? In my canvas, the link of the videos will be posted which will take the students to your channel. Thank you.

[@ProfessorDaveExplains]

Of course, link away!

[@dansheffield4021]

I just did the same! Best video I could find for my Geometry class while I'm out sick!!

[@andresb9006]

Man you are awesome!!!! You have a gift in ecplain8ng things, thnks a lot!! One of the best videos I've seen about this topic! Regards and my vest wishes, I am a fan now.😀

[@sowmiyafarhath807]

Sir,can you explain me? In checking comprehension how 600° = 4π/3

[@ProfessorDaveExplains]

once around is 360, so that's 240 left

[@sowmiyafarhath807]

Thank you sir....

[@carultch]

@@sowmiyafarhath807 600 degrees = 10*pi/3. You can type in "600 degrees to radians" in Google's search bar to see that this is true. Then multiply by 3/pi, and you will get the number 10. It doesn't strictly equal 4*pi/3 radians, but it is an equivalent co-terminal angle to 4*pi/3 radians. The reason why this reduces to 4*pi/3, is what happens when you subtract integer multiples of 2*pi, to reduce the angle to an angle less than 360 degrees, and determine an equivalent angle. Not an equal angle, but an equivalent angle. 10*pi/3 - 2*pi= 10*pi/3 - 6*pi/3= 4*pi/3

[@ayaansiddiqui3086]

Trigonometry is not in my syllabus but still I am learning it for competitive exams. Your videos are very useful

[@YeshuaIsTheTruth]

You sound like an awesome smart guy. Keep it up, bro bro :)

[@ayaansiddiqui3086]

@@YeshuaIsTheTruth are you a student

[@lauramoreno8742]

His vids are the best and most uncomplicated on KZbin

[@adhiyanthaprabhujeyashanka2091]

Please clarify Hi professor dave, in checking comprehension, (600degrees to radians) when converting we multiply 600 by π/180 so that must be 10 over 3 times pi(π), please

[@carultch]

600 degrees = 10*pi/3 radians It doesn't strictly equal 4*pi/3 radians, but it is an equivalent co-terminal angle to 4*pi/3 radians. The reason why this reduces to 4*pi/3, is what happens when you subtract integer multiples of 2*pi, to reduce the angle to an angle less than 360 degrees, and determine an equivalent angle. Not an equal angle, but an equivalent angle. 10*pi/3 - 2*pi= 10*pi/3 - 6*pi/3= 4*pi/3

[@kanishk2082]

Wait so 10pi/3 is wrong?

[@kanishk2082]

Oh wait nvm I understand now

[@samphorsleng98]

the radian is =57.3°

[@蔡骁驰]

蔡骁驰 0秒钟前 In a numerical sense，the equation 5/4pi is not equal to negative 3/4 pi coz 5/4 is not equal to negative 3/4. I think what you want to express is that in the trigonometric system defined by the unit circle, angle 5/4 pi is logically equivalent to negative 3/4 pi.

[@mustafasaber5076]

From r to d : 120° -425° 900° 1680° From d to r : 7/4 pi Pi -3/4 pi 3 pi

[@thatgamerboy3467]

"Do not fear my child, for i am the light" - *math* jesus

[@HelloHeloWorld]

Are you sure about the last question? 600 degrees is not 4pi/radian, according to my humble calculations. I got 10 pi/3 and I checked online, seems about right.

[@cyklone5000]

As it turns out, 360 is divisible evenly by every single-digit non-zero integer except 7.

[@78anurag]

Poor 7 :(

[@carultch]

We'd need a 4 digit number to include 7 in that list. If we had 420 degrees in a circle, we could divide it by the first 7 consecutive whole numbers.

[@jovanabogdanovic2680]

@@carultch lets turn this into a petition to change it

[@mr.meeseeks6549]

Bro my professor made us learn what everything was and what they meant online, which was easy; and when I went to class, he made us come up with formulas and then I thought this class was hard lol tbh he didn't even teach us until after everyone was done solving the problems, and I felt dumb cause most people knew what to do.

[@siratalmustaqeem7672]

Sir in comprehension radian to degree 5π/2 = 450 Na and 14π/3 840 , is it right or wrong and if it is wrong plz tell me how Bczo first two questions I have done in same way and I get right answer.... Plzz reply

[@ProfessorDaveExplains]

yep that sounds right!

[@meerohalfalasi9249]

sir i cant understand this part and i have exam tmmrw so can u help me plzz ansswer @@ProfessorDaveExplains

[@YeshuaIsTheTruth]

@@ProfessorDaveExplains I really appreciate how thoroughly you explained this topic, but the practice questions at the end don't make much sense. The video says that 14pi/3 =120deg... but 2pi/3 = 120deg on the diagram you gave us.

[@ProfessorDaveExplains]

2pi brings you back to zero

[@YeshuaIsTheTruth]

@@ProfessorDaveExplains pi = 180, so 2pi = 0, but then 2pi/3 would be 360/3, right?

[@kendyangue3678]

Sobrang galing mo talaga, Professor!

[@MIZORAM_mafaka_hnamte]

*_I wish teacher like Prof. Dave are in every High school and college_*

[@anjaiahkandula7538]

Dave is God of knowledge. Long live you.

[@MingHenn]

Hi sir I am some question about the exe sir gave which the question -7pi/6 how to calculate to get the degrees for 150?

[@anthonystark6215]

Thank you, Professor!

[@bluesteelgaming2883]

After 13 years away from school, I took my final algebra course a couple years ago and did well. To make sure i dont struggle trying review algebra while studying trig, what is the most important material to refresh between now and then?

[@mangmangsarahjeany.5258]

Thanks prof, I need it rn❤️

[@darktreehousea9081]

I finally understand this thank you

[@russellrohde8598]

Might just be me, but unless i'l trying to do trig using Excel or a programming language like C (example), everything is done using degrees - not radians. Coming from 'not-america', I can say that math in high school, the electrical trade and dip. electrical engineering uses all degrees - not radians. Seems somewhat unnecessary to use radians for trig. I've never used it teaching trig, vectors, wave addition or anything else associated with sine, cosine or tangents. Only ever used it when programming and only when converting from degrees to a make a program language function operate so I could then convert back to degrees - we all speak in degrees anyway. All that said about radians, thank you for the vid. After decades of stuffing with conversions when programming, I now know what I am converting - Gives me another arbitrary thing to nerd out about at the pub with my mates!

[@navjotsingh2251]

I'm from the UK and i learned trigonometry using radians.

[@ikemuoma8495]

To me, Radians only make sense if one is talking about multiple rotations of the unit circle. Other than that, using degrees seems the easiest. Especially when dealing with angles of a triangle.

[@appahoopjack2514]

Electrical Engineering does NOT use Radians in USA??? Not extensively, but it's there... Calculate Capacitive & Inductive Reactance

[@carultch]

The reason we use radians for trigonometry, is that it makes the Calculus of the trig functions A LOT more elegant, when compared to any other units. It also allows you to track arc length, just by multiplying the angle and the radius, rather than also needing to convert units. Formulas in Physics such as Power = torque * rotational speed work out elegantly when rotational speed has units of radians/second. But you end up needing conversion factors when you use degrees per second, or revolutions per second. For instance, when you take derivatives of sin(x), you end up with a cycle of derivatives that repeats itself, when you use radians as the units. Derivative of sine is cosine. Derivative of cosine is negative sine. Derivative of negative sine is negative cosine. Derivative of negative cosine, brings us back to sine. When you introduce degrees as the units of this function, you end up accumulating a pi/180 factor, every time you take a derivative. This makes it a lot more complicated with all the further applications of calculus and trigonometry together.

[@brett54]

hmm.... Degrees measures the angle from a stationary observer at the center looking out at a moving target. Radians (really a distance measurement), is with a moving observer looking back at a stationary target. I also find using multiples of pi/2 (or 90 deg), more intuitive; pi/2, 2pi/2, 3pi/2, 4pi/2 around a circle.

[@prabjeetsingh4768]

Last comprehension question's answer should be 10pi/3

[@fireball0762]

Thanks professor, I am hoping to add math to my teaching license, and i need trig before i take college calculus

[@rheiagreenland4714]

Our school's online curriculum (a *lovely* little website called Odysseyware) decided to have us use trig functions to solve for missing sides of a triangle without touching on radians at all or how to configure a calculator to use degrees instead. Which kinda breaks triangles when you get negative numbers from these functions. Sigh.

[@iansvoice1]

Does the size of the circle effect a radian? Or will 1 radian always stay constant? For instance, would there be a difference when measuring a radian from a circle with a 5 inch radius compared to a 10 inch radius?

[@ProfessorDaveExplains]

No because it's an angle.

[@iansvoice1]

@@ProfessorDaveExplains Right, that makes sense. Angles stay the same no matter how long the lines are. Perhaps I more concerned with arc lengths and how radians apply. I work in aerospace with rotational parts and arc lengths come up a lot especially when manufacturing the part on a machine. My brain wants to connect radians to arc lengths. Where am I going wrong? Or am I just missing something?

[@ProfessorDaveExplains]

@@iansvoice1 Well sure, arc length will change. Just not angle. Remember that radians are angles, not lengths.

[@iansvoice1]

@@ProfessorDaveExplains Roger that! You’re a legend btw for answering questions on a 4 year old video. Love all of your debate content on flat earth! More over, this back catalogue of educational content you have available is really handy. Thanks for that!

[@nimaemami6709]

Love the tutorial

[@tazziiiee]

At 5:45 the answer for 600°=4π/3 However.... Formula for converring degrees to radians=value in degrees x π/180 Solution=600 x π/180 =10 x π/3 (factor of 6) =10π/3 howcome 4π/3??

[@Yahya1990-g5m]

I have the same question? How

[@carultch]

600 degrees = 10*pi/3 radians. It doesn't strictly equal 4*pi/3 radians, but it is an equivalent co-terminal angle to 4*pi/3 radians. The reason why this reduces to 4*pi/3, is what happens when you subtract integer multiples of 2*pi, to reduce the angle to an angle less than 360 degrees, and determine an equivalent angle. Not an equal angle, but an equivalent angle. 10*pi/3 - 2*pi= 10*pi/3 - 6*pi/3= 4*pi/3

[@HermioneGranger-x3x]

How did 600 deg become 4/3pi? I thought it's 600/180=10/3 pi?

[@gamingwithrksaver4868]

Pi/2 is 90°... Something wrong in 3rd of 1st question?

[@OkSid300]

Must be the easiest comprehension section in my life. And I remember how I screwed up in simple division. I wonder if the rest of trigonometry will be that easy...

[@muratbilir4240]

According to your explanation radian is an unit for angle like degree. But in some proofs like lim x>0 sinx/x it is treated like length, as it is simplified with length. (by squezing method)I will never be able to understand what really radian is.

[@ProfessorDaveExplains]

It’s an angle. Visit my earlier trig tutorial explaining radians.

[@YeshuaIsTheTruth]

How does 14pi/3 = 2pi/3????? I r confussed.

[@ProfessorDaveExplains]

2 pi brings you back to the origin, so every multiple of 2 pi is the same as zero.

[@YeshuaIsTheTruth]

@@ProfessorDaveExplains OOOOOOOH!!! That's so cool! So 2pi = 4pi = 200pi!?

[@Smile-wr2jc]

Why is 600⁰ equal to 4pi/3 in radians?

[@carultch]

It's not strictly equal to it, but it is an equivalent angle to it. If you type 600 degrees to radians in Google Calculator, you will see that it equals 10*pi/3. However, when you subtract 2*pi from 10*pi/3, you will get 4*pi/3. Depending on application, 10*pi/3 is equivalent to 4*pi/3, since it is an equation with the same terminals. One contains another revolution, if it is of interest to your application to keep track of revolutions. But it is common that we are only interested in the modular arithmetic of radians, and reducing them after every full revolution. Again, it depends on application. In a physics problem where full rotations matter, they are not equal, as rotating 240 degrees is a lot different than rotating 1 rotation plus another 240 degrees, even if the rotating body ends up in the same position in the end.

[@ruskinyruskiny1611]

"When I think back on all the of crap I learned at High School, it's a wonder I can think at all". Paul Simon.

[@MiltosPol-qn3zh]

TRIGONOMETRY!!!!!!!!

[@user_z11]

54ígñœmë546

[@carultch]

It should really be called kuklometry, to reflect the fact that it is defined from circles for all angles.

[@Roswaltt]

And i still manage to not understand anything in the Radians part nice 💀

[@Roswaltt]

I just love how I dont understand anything in the vid, I hate this

[@ProfessorDaveExplains]

start from the beginning of the trig playlist to learn about radians

[@coyvaultboy4272]

its the beginning tho@@ProfessorDaveExplains

[@IbrahimKwakuDuah]

I think Prof didn't help by writing 180° = π I found that statement worrisome till I watched it like 3 times to notice he said he'll assume π=πr. So 180 is actually rπ and not pi in literal terms

[@蒙贵子]

你说的 这个例子，弧度r长度一定等于半径r吗

[@celestecelestialcharity6662]

how did 315 degrees= 7pi/4? can someone please help me understand :'(

[@ProfessorDaveExplains]

Watch one more time from the top.

[@carultch]

This is an easy one, because it doesn't require adding or subtracting 2*pi at the end, like some of his other check comprehension examples. Write down what we are given: 315 degrees Multiply by one, in a fancy way, in order to cancel the degrees. pi radians = 180 degrees 1 = pi radians/180 degrees 315 degrees * (pi radians/180 degrees) = 315*pi/180 radians Reduce the fraction, 315/180, and we get 7/4. Identify factors in common between 315 and 180, and cancel these out. We can identify 5 as a common factor, because they both end in either a 5 or a 0. (315/5)/(180/5) = 63/36 We can identify 9 as a factor of what remains: 63 = 7*9 36 = 4*9 Thus our fraction becomes: 7/4 Include the pi radians we originally had, to get our answer: 7*pi/4 radians

[@topiado2073]

Sir please where can i get geometry lesson??

[@ProfessorDaveExplains]

check my geometry playlist! or just scroll down on the mathematics playlist

[@topiado2073]

@@ProfessorDaveExplains ok sir

[@hughjanuz4343]

got confused with 5/2pi when converting from radian to degree, I always get 450

[@HelloHeloWorld]

Your calculations are correct. However, 360 is a full circle, whenever you see a number extending 360, it means you need to subtract 360 from it, because it means you completed a full circle, and starting over, so 450 - 360 = 90 degrees.

[@rihyanny]

​@@HelloHeloWorldThank you for this, I was having a hard time to understand why it was 90° lol🥲

[@HelloHeloWorld]

@@rihyanny No problem! Stay strong and good luck on your math journey! :D

[@bachairnoore7359]

;)thank you very mush :)

[@davidbailis8415]

Wouldn’t it be that coterminal rays are two rays with a common end point, not start point

[@tGoldenPhoenix]

Done.

[@bmzaron713]

The easiest way to convert between degrees and radians: just multiply by pi/180 or the inverse

[@khagesh2116]

😎 cool

[@Bigman-om4zc]

i guess i basically skipped 11 grade due to covid allowing online school and me cheating. Decided today to learn trig lmao. Thanks for this possibility

[@TruckerCarlson]

or use the square of the hypotenuse and forego all that...

[@fahadshaikh5686]

Maybe in comprehensive the question in convert degree to radian the 600 degrees=10/3π 😅

[@aiueo8962]

I think if degree is > 360, the degree must be substract by 360 several times to get x < 360. Then... 600-360 = 240 240/180 = 8/6 = 4pi/3. Is ez when you slowdown...

[@janrielarnoza4094]

Thank you for this lesson Papa Jesus❤️

[@celestecelestialcharity6662]

wait what?! how did 5pi/2 = 90 degrees? my answer is 450 degrees :'(

[@ProfessorDaveExplains]

What's 450 - 360?

[@celestecelestialcharity6662]

@@ProfessorDaveExplains oh I see, Thank u sir.

[@jack6478]

Oh boy time to break my brain!

[@jamiladatumolok8181]

the answer at the end are incorrect

[@topiado2073]

Sir I'm big fan u

[@patrikopsprerov2630]

The answears at the end doesnt make any sense. Even online calculator returns diferent answers.

[@ProfessorDaveExplains]

check your calculator mode

[@aminmkyt4191]

From last night I have been thinking how can 18 degreed be pi, and today after half an hour i realized that it was 180 degrees :/

[@josephmahi-o4e]

HALLO

[@dutchatheistc.3399]

I don't understand it. Why would anyone downvote this

[@Adam-cn5ib]

Maybe they don't understand it and get frustrated.

[@pymuno5443]

@@Adam-cn5ib maybe it's the way he explained it. He made it more difficult than it should be. (I didn't downvote the vid, but there are easier ways to explain the concepts)

[@kanishk2082]

Guys isnt the last one’s ans wrong I got it as 10pi/3

[@sanaesceptico]

Yes

[@OW0974]

Me who already knows what it is: mm yes new functions

[@AsmaAsma-om7yw]

This is can I useful in physics!!?

[@Adam-cn5ib]

Trig is extremely useful in Physics.

[@Kaiju3301]

If you aren’t good with trig you will die in calc and physics.

[@tabbyblu771]

I still don't know what a radian really is

[@samjames1253]

Kent Hovind: "you see Dave, in the bible...."

[@carultch]

There is a passage in the bible that people believe indirectly says pi is exactly 3. It describes a circular object that is 10 cubits across, and 30 cubits around. It might seem like it states pi is exactly 3, but the given data is only accurate to one significant digit. If you don't know what a cubit is, the modern consensus is that it was 18 inches, or 457.2 mm.

[@Teluguspacechannel]

your voice is so sweet

[@AlessandroZir]

❤❤❤❤❤👌

[@velastemandipashielamhae4286]

Math Jesus

[@randomfatkidonyoutube1400]

For 5pi/2 I got 450°

[@ffnoobx3214]

Same but why 😓

[@grislaurent4131]

how the fuck do i understand this here but not when our teach explains it

[@jaysonwild4899]

Wait. What?

[@Ghulamnabi-g8v]

Which is watching 2024

[@stairwayunicorn4861]

IMO degrees should be abandoned as units because of how non-intuitive it is.

[@jasonyoung8963]

This one sucked!

[@HermioneGranger-x3x]

How did 600 deg become 4/3pi? I thought it's 600/180=10/3 pi?