How to determine the point on the unit circle given an angle

👉 Learn how to find the point on the unit circle given the angle of the point. A unit circle is a circle whose radius is 1. Given an angle in radians, to find the coordinate of points on the unit circle made by the given angle with the x-axis at the center of the unit circle, we plot the angle on the x-y-coordinate plane and with the help of Pythagoras theorem or the special angles, we can determine the point on the unit circle made by the given angle.
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Organized Videos:
✅ Trigonometric Functions and The Unit Circle
• Trigonometric Function...
✅ The Unit Circle | Learn About
• The Unit Circle | Lear...
✅ Points of the Unit Circle | Learn About
• Points of the Unit Cir...
✅ Angles of the Unit Circle | Learn About
• Angles of the Unit Cir...
✅ Trigonometric Functions of the Unit Circle
• Trigonometric Function...
✅ Find the Point on the Unit Circle
• Find the Point on the ...
✅ Evaluate Trigonometric Functions Using the Unit Circle
• Evaluate Trigonometric...
✅ Evaluate the Six Trigonometric Functions Given and Angle
• Evaluate the Six Trigo...
✅ Evaluate trigonometric functions using a calculator
• Evaluate trigonometric...
✅ Evaluate trigonometric functions using identities
• Evaluate trigonometric...
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvi...
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[@raeallen2708]

I can’t believe my tuition is 12000 a year and this free video did more for me than my $1500 pre calc professor 🙃🔫

[@yuhhhhhhhhhhhhhhhhhhhhhhh]

same except my tutition is $30,000 * cries in dumb *I

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[@TLathers225]

Bruh facts

[@tracy_cakkes]

Same smh

[@adrimakesmusic2997]

1:39 That is the best human-drawn half circle that I have ever seen!

[@Anonymous-hv2zc]

bro, ngl i was like 🤯

[@yuhhhhhhhhhhhhhhhhhhhhhhh]

Given the fact that we are doing online college and I haven't seen my professor's face this whole semester.. this saved me because I have been working on the topic for 3 days now on my own and I was close to throwing in the towel.

[@octopudding]

I have a midterm today (its 1am rn) and im just now understanding how to do this thanks to this guy. it doesnt help that my precalc class is a mini session class so it covers twice as much in a week ;-;

[@Kaijuzilla621]

Did Israel get it though?

[@user-pj2ti4ms8p]

I just learned more in 6 minutes and 27 seconds than I have for the past 5 days. Thank you!!!

[@Harveyspecter227]

you've been saving my life since highschool. thank you for your service

[@lacylaplante]

You're an amazing teacher! Thank you!

[@danielasmite7859]

This made everything more clear. Thanks!

[@kaliekrobinson2987]

⁠​⁠ You’re a phenomenal teacher

[@ellaahanene2189]

Omg you draw perfect, you teach perfect!! I literally love you!!

[@sarah.3599]

But what if the denominator is a number that is not on the unit circle? Example: sin 8pi/7. How would you do that?

[@eshaghazali2954]

This was beautiful! Completely understood

[@JonasKaunKrafts]

this gave me more than a 45 minute video i just watched and the entire unit information in my class

[@deleted-user-82u3ht92]

that dollar analogy is god tier. you are a blessing to anyone you teach bro

[@Heccadunks]

I watch your vids instead of going to class... I learn better here 🙏 thanks G!

[@adityaparmar5877]

I was so confused but soon as I watched your video I got it. You are the man. Thanks!

[@AmelieOnline]

But then how do I find the point if my reference angle is not 30, 60 or 90 or any of those standard reference angles

[@brianmclogan]

Find the positive acute distance to the x-axis

[@VanessaPartidaiAMHealthynFit]

wow! you teach math like no other math teacher! Thank you!!! It was very helpful!

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this guys my favourite

[@arizona6288]

That was the best explanation ever thank you!

[@VanessaPartidaiAMHealthynFit]

agree!!

[@sachinfitness3932]

Your explanation method is very clear sir.

[@jamesparkinson6876]

Wow that made more sense than a lot of the text books I have read over the years.

[@jpm5965]

You're my Dawg

[@enesislami8734]

I wish you were my professor you are too great and thank you very very much because I never understood how all of this works thankssss so much you are the best explainer that I ever saw this far thank you!

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Brian McLogan for president

[@MFblas]

How did you manage to make me smile ear to ear while finally figuring out this concept? : }

[@brianmclogan]

This comment makes me smile ear to ear

[@MFblas]

@@brianmclogan Thanks professor! You rock!

[@yassoamin1452]

What long explanation this was the shortest best explanation I have had until now

[@brianmclogan]

Good?

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You're the man!!!

[@derekdan2170]

eso me ha ayudado tanto, muchisimas gracias

[@DRWP10]

thank you

[@zyllestose2791]

this made me understand it better, but how do you state which quadrant it lies on?

[@expression3639]

Probably too late, this being a year later, but I will answer anyway. Mentally divide the circle like he explained at the beginning according to the denominator and start counting counter-clockwise if the point is positive or clockwise if the point in negative.
So for example, -5PI/4 : You divide the top half in 4 and the bottom half in 4. Then you count clockwise because the number is negative ; 1, 2, 3, 4 (now you've arrived at the top half) and 5. So 2nd quadrant.

[@andrewbedolla51]

THANK YOU!!

[@danielbailey6923]

You make this so easy, thank you so much

[@masturdOfTheUniverse]

04:50 Why are the denomintators 2? Why are we doing this little fun thing applying numbers to the numerators? Where do they come from?

[@bobbercat2250]

You saved my life

[@reold]

Ty!

[@chandacherrubleo8837]

👏🏽👏🏽Why do others make it so complicated 😭

[@sanvisharma8521]

Amazing 😭❤️

[@carmelrobles2888]

so helpful

[@katlegomodiga1264]

You're the best thank you!!!!!

[@arieleaston332]

thank you!

[@oxiyne3487]

i couldn’t learn this in my thousand dollar college pre calc course but i could from a random professor on youtube for free….

[@adrianhull469]

lifesaver

[@Lily-zc5gu]

What if the numerator is 113 and the denominator is 2 ? Is there some equation for this ?

[@jasminefitzsimons896]

I GET IT NOW OMG

[@goodnightvids]

That’s a great semicircle 😃

[@brianmclogan]

thank you!

[@goodnightvids]

No thanks to you you’re the greatest teacher I’ve never had🙏🏻

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i wish u were my college professor omg

[@brianmclogan]

Happy to help!!

[@Onyx8Moon]

cool!!!

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i love you

[@thelabperson7651]

What point would be 59 degrees?

[@kaihuynh8145]

I am speechless

[@kimberlygarcia142]

I’m genuinely confused still, why does it end up being 6pi on this case?

[@kimberlygarcia142]

Nvm kept re watching it now I understand thank you!

[@ziondapaa6392]

feel like the blindfold has been taken off

[@thatomofolo452]

🙏🙏🙏

[@itsalternation9102]

Do you know how to do this on their face of a 3d circle

[@billjamal4764]

Free my boy Ryan he aint done nothing

[@richardpineda2904]

The Fuck I just get confuse with the last part. You made a right angle but the sections have more degrees than to a right angle

[@lunaeclipse5768]

NACHO VARGA

[@zachsmith5643]

This still confuses me. How do we find where the x and y coordinates come from? I have questions in my homework that ask me to find the points but no one explains the math behind finding them. Were just "supposed to know" what they are and it's making it really frustrating for me because I can't remember every x and y value for every angle in the unit circle. Someone please explain this to me

[@expression3639]

Too late, but I will answer anyway.
A unit circle is a circle where the radius is equal to 1.
So you have a circle with a radius of 1. Then you have an angle that starts at 0 (think of a protractor) and the other leg of that angle lands somewhere on the circle. Let's have you mentally picture a 45° angle for the sake of it. At the end of that leg, marking the 45° angle, is a point. Now if you will notice, this gives you 2 points. The middle of the circle and the point at 45°. From the 45° point, mentally draw a height all the way down to the 0° leg and form a right triangle.
From all of this, you know 2 things about this triangle. The hypothenuse also represents the radius of this circle and because this circle is a unit circle, you know that its radius is 1 so the hypotenuse is also 1. You also know one of the angles, which is 45°. Using this, you can use trigonometry to find the length of each of the other sides of this triangle. The vertical (opposite) side represents the y coordinate and the horizontal (adjacent) side represents the x coordinate.

[@expression3639]

He has a video here : ruclips.net/video/TGSyMkR6VbI/видео.html

[@miraygungor8296]

@@expression3639 thank you very much. i am an incoming college freshman and this comment helped me a lot.

[@heijeol.1793]

why i dont get it 😭😭

[@bearmouse9424]

I am not understanding this at all

[@richardpineda2904]

Fuck it forget about it

[@leafyzzz]

thank you