Unit Circle Trigonometry - Sin Cos Tan - Radians & Degrees

This trigonometry tutorial video explains the unit circle and the basics of how to memorize it. It provides the angles in radians and degrees and shows you how to evaluate sin cos and tan.
Trigonometry - Basic Introduction: • Trigonometry
The Unit Circle:
• The Unit Circle, Basic...
How To Remember The Unit Circle Fast:
• How To Remember The Un...
Reference Angles:
• How To Find The Refere...
The Six Trigonometric Functions:
• The Six Trigonometric ...
How To Solve Right Triangles:
• Trigonometry - How To ...
_____________________________
Reciprocal Identities:
• Reciprocal Identities ...
Quotient Identities:
• Quotient Identities - ...
Even and Odd Trigonometric Identities:
• Even and Odd Trigonome...
Pythagorean Identities:
• Pythagorean Identities...
The Pythagorean Theorem:
• Pythagorean Theorem - ...
Trig Functions - Periodic Properties:
• How To Evaluate Trigon...
________________________________
The Exact Value of Trig Functions:
• How To Find The Exact ...
Special Right Triangles - 30 60 90:
• Special Right Triangle...
Special Patterns - Pythagorean Theorem:
• Special Patterns of th...
Cofunction Identities:
• Cofunction Identities ...
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Trigonometry Formula Sheet:
bit.ly/47diggI

[@TheOrganicChemistryTutor]

Trigonometry Formula Sheet: bit.ly/47diggI Final Exams and Video Playlists: www.video-tutor.net/ Trigonometry - Basic Introduction: kzbin.info/www/bejne/nWm5dHuliNBoldE How To Graph Trig Functions: kzbin.info/www/bejne/nIKzgHWFe8dlqbs Evaluating Inverse Trig Functions: kzbin.info/www/bejne/qaCchZ2ha6yUaLc Verifying Trigonometric Functions: kzbin.info/www/bejne/hHaZq5aAiL-bjpI Trigonometry Final Exam Review: kzbin.info/www/bejne/hXLWk6tqiaqhgpI

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[@sanopann1896]

bro can i ask for help at 32:17 why the negative leave behind in the numerator

[@astroh8674]

@@sanopann1896 I’m pretty sure you can’t have a negative numerator ?

[@oldHavenNicholsishere]

@@astroh8674 That becomes negative for the entire fraction I think....

[@SweatBloodTears]

Had same question @@sanopann1896

[@RackUR]

@@sanopann1896 The negative can be anywhere, in the numerator, denominator r the middle and it'll be the same result

[@meganhamilton8879]

When your teacher makes no sense but this completely does. Thanks for saving my grade.

[@gameswithricky1264]

The fact I was able to memorize the unit circle entirely in 10 minutes with just this video is incredible. Thanks so much

[@hi-hc3ms]

you didn’t need to memorise the unit circle 💀.

[@gameswithricky1264]

@@hi-hc3ms I needed to cus I wanted to skip algebra 2 and it was the only thing I was unsure about

[@ZhiwaJ]

@@hi-hc3msit’s actually very useful for the first and second derivative test for trig functions

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[@sherenemichaels4738]

The unit circle is just a way of adding 30ths and fifteens to the number that comes immediately before it in order to get the next number After zero we add 30 After 30 we add 15 to get 45 After 60 we add 30 to get 90 After 90 we add 30 to get 120 After 120 we add 30 to get150 after 150 we add 30 to get180 After 180 we add 30 to het 210 After 240 we add 30 to get 270 After 270 we add 30 to get 300 After 300 we add 30 to get 330 After 330 we add 30 to get 360 The addition of fifteens comes inbetween The numbers directly before and after 0, 90 180 270. We add thirties To all the others we add fifteens 30, 150 210 330 all have sine and cosine coordinates of square roots of three over two and 1/2 ...... In some variations or other depending on which quadrant they are in they may be positive or negative Remember that sine is mapped to the Y axis while cosine is on the X axis ( COSINE, SINE) This way you can learn the unit circle just by adding fifteens and thirties to preceeding numbers to get the current number if you study it a bit Not want to bore you anymore by teaching you many more methods to learn the unit circle I am Richard Michaels Younger brother of Shereen Michaels and I am a student at SUNY in New York USA Cant give out my email address here Too public Would love to help more if I could Sorry

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thanks so much for this video omg I have had several people try to teach me to understand the unit circle and I never ever get it but this made me understand

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This was so helpful to me, I was consumed by these problems in the class as I was the only one unable to do this and had hesitance to ask the teacher such a basic thing

[@alumi9818]

13:40 really important to memorise 23:00 better method is to think about pi/6 instead of 5pi/6 and just multiply it by 5 - so: pi/6 = 30 so 5pi/6 = 150

[@mxlxzybbb]

Why multiply it by 5???

[@yuji3171]

I did sin ( 5pi/6) in my calculator and it does not equal to 1/2

[@bigfgreatsword]

@@yuji3171 If you are using the 580X Casio, there's a OPTN button, for degree to radians conversion, it's the little r, hope this helps!

[@yuji3171]

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[@Phoenix-np1iu]

Yeah just remember 0 degrees to 90 degrees and go from there more or less

[@EternityMoix]

Better way to memorize this, Sin30 = 1/2 Sin45 = sqrt2/2 Sin60 = sqrt3/2 Cosine is just the opposite, Cos60 = 1/2 Cos45 = sqrt2/2 Cos30 = sqrt3/2. If you look at this the Sin values goes from least to greatest, and Cosine values goes from greatest to least. Regarding Tangent, its just Y (sin) /X (cosine) or Opposite / Adjacent, Tan30 = 1/sqrt3 = sqrt3/3 Tan45 = sqrt2/2 / sqrt2/2 = 1 Tan60 =sqrt3/2 / 1/2 = sqrt3 For reference angles just remember if the given angle is closer to 180 or 360 degrees or Pi / 2pi. When in radians for example if given Cos(2pi/3) you can ignore the 2 and just focus on pi/3 since thats the reference angle. Thus becoming Cos(pi/3) = -1/2 since quadrant 2. Remember your Quadrants Q1,Q2,Q3,Q4 and also just remember A S T C regarding the positive values for the trig functions.

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Thank you, thank you, thank you !!! Now I can see the relationships, rather than learning reference angles in isolation, WOW !!!

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Please explain further

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all students take calc

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Explanation

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I know what this means Pay attention to the first letter of each word: *A*ll *S*tudents *T*ake *C*rack Quadrant 1 - All values will be positive Quadrant 2 - only Sine values will be positive Quadrant 3 - only Tangent values will be positive Quadrant 4 - only Cosine values will be positive Rmb to go anti-clockwise

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how'd it go?

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Alexis Malagotnot what specific test were you studying for?

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[@musabizimana3587]

9 minutes in and I already have learned soo much. Is it better to memorize unite circle?

[@mountcarmel7116]

before showing all the pre calculated numbers, why don't you show how these numbers come from.

[@Kalliegurl]

You make a valid point, but try doing a little extra research outside of this video and combine that info with this one. That's what I did and it all came together to make sense eventually. I hope this helps you.

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he actually did in one of his other video.... forgot which one though

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[@sgedeon01]

Around 9:20 you wrote that the hypotenuse = 2 for the 30-60-90 degree triangle. This is incorrect. The hypotenuse of a triangle on the unit circle is always = 1 because the radius of a unit circle is always equal to one. Also the 30-60-90 degree triangle is half an equilateral triangle. So given that hypotenuse = 1 (since the triangle is on the unit circle) and Pythagorean theorem you can get the other sides. So the sides of 30-60-90 degree triangle on unit circle are: hypotenuse = 1 Side = 1/2 Other side = (sq. rt. 3)/2. Same hypotenuse = 1 concept applies to 45-45-90 degree triangle since it’s on the unit circle. This means that hypotenuse for 45-45-90 degree triangle is (x)(sq. rt. 2) = 1. And the two other sides of 45-45-90 degree triangle are each 1/(sq. rt.2).

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Chemical here

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[@cesar_br5848]

I prefer use the rule of "Use sempre sua cabeça", or USTC. That's a portuguese shortcut to know where is the signal from the cos sin ou tan of a given angle If the angle is from the 1st quadrant, it's always positive from the 2th, only the sin will be positive the 3th, the tangent and the 4th, the cos Of course, your way is very practical to lear if we are dealing with non exact angles (like tan of 572 degrees, which can be expressed in radians instead of degrees). To sum up It could be useful kowing how to use both of them!

[@CaseyMarkov]

21:43 "if you put it to your calculator it will say 'what are you doing?'" I found this funny for some reason

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I had a test on this today that determines whether I graduate high school or not. Thanks to you, I will be graduating with my class. Thank you so much!!! 2.3K Reply

[@DarsiDarsi-]

Why’d you copy paste?

[@bgpcusercheater5174]

@@DarsiDarsi- how did you know?? 😮😯😲😨😱.. jk, I was not doing it with any ulterior motives, anyone wod know it is copy paste

[@DarsiDarsi-]

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[@gonzaloluna1989]

Thanks a lot. It is starting to make sense. I am still struggling of how the special triangles got their values(like for the 30 degree triangle 1, square root of 3 and 2 for hypotenuse). I know that they are used in the unit circle. I am memorizing it but I would like to know how those three values were arrived at. Thanks again

[@lonesegotlong459]

They were derived from the unit circle.

[@levixhange7989]

I love that there's a background sound of the rain shile you're recording this.

[@Billy-jb2xc]

I noticed a error in the triangles at 9:30/59:25 60 degrees and 30 degrees should be switched around so that 60 degrees is on the bottom and 30 is on the top. Hope this was helpful despite it being 3 years :)

[@NanaWasHeree]

Isn't it already correct as 30 has to be opposite of side length ratio 1 and 60 opposite of side length ratio root 3.. It doesn't really matter what's on the top and bottom as long as the ratios are right.

[@judahb3ar]

@@NanaWasHeree Billy's comment is incorrect, the video has the correct reference angle. Although yes, you are right, it doesn't really matter in this case what is on top and bottom as the ratio is the same. But the idea is to make sure the reference angle is the angle of the hypotenuse with the x-axis, which is what is displayed correctly in the video.

[@rainware1804]

holy man, thnak you so much now i understand it much better than my math teacher explained it

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dude i love you. you made this shit make sense for the first time in my life