14 - Reference Angles Explained - Sine, Cosine & Unit Circle - Part 1

In this lesson, you will learn what a reference angle is and why they are important in trigonometry, precalculus, and calculus. A reference angle is the angle measure from the terminal ray of the angle to the x-axis. It is always a positive angle. The reason we use reference angles is because the sine and cosine (sin & cos) of any angle around the unit circle can be found by examining the corresponding reference angle. In other words, the sine and cosine ratios are the same values all around the unit circle, and the magnitude of this value only depends on the reference angle. We then apply the correct sign to the final answer depending on what quadrant the original angle is located. In this lesson, we will draw an angle, find the reference angle, and discuss how to find the sine and cosine of the angle using its corresponding reference angle.

[bryankervin]

Thank you for your service, this is so understandable. I was about to drop this class but you make me change my mind Thank you once again sir.

[antonin]

Great explanations, before actually doing the applications! The pacing, organization, drawings and writing are perfect!

[janetlento]

Wow, I cannot thank you enough—you made this so understandable! Please continue to make these videos; they are so helpful.

[TijwokPeter]

Thanks for this great effort you made to us in this video..

[WolfPup-gbze]

You always have really good videos. Very thorough. Thank you!

[simpleman]

I was paying attention while watching your lesson on the unit circle. You hinted to the reference angle to the X axis. Here I'm only learning the word prime.
I watch your videos over and over and over, then something will become so obvious, like I should have known all along.

[TheRelatableProfessional]

As an A level teacher myself, I take my hat of to you. You are excellent!

[laurachitez]

You are a very generous person, thank you!

[ahmadmadhi]

You actually deserve more than 1m likes, thank very much for solving my problem ..!!

[sagarprajapati]

i m from india nd i m watching your lecture...thiss is soo owsm...hlp us lot..thankyou sirji🙏

[hemarajue]

I think trigonometric values remain the same either we move clockwise or anticlockwise observing the quadrant rule of signs.
We have two trig. identities Ie sin(-β)
.=-sinβ
cos(-β)=cosβ Is β is an acute angle?

Practice is not necessarily doing the same thing repeatedly rather it is seedling and cultivating some good habits.

[denvercharlebois]

What if the reference angles aren't special triangles like 30, 60 and 45? How would I go about finding the values of the sine and cosine? Anytime I input it I get a crazy decimal number how do I go about finding it in fraction form?

[abrahamkatongo]

thank you very much for helping me you mean a lot to me. GOD bless you.

[axmedyare]

Thank you sire I understood really thank you again

[cosainaliyahm.]

You're so helpful sir! Keep up the good work :)

[astroporpoise]

Thanks so much for your clarity and thoroughness! :)

[eslamelsofany]

thank you mr jason
when you continue ac circuit courses??

[reginajohnson]

Is a 315° a 1.75 I divided that by 180°

[nnekromant]

I LVOE YOU THAN KYOU FOR SAVING ME ILY

[grenadaveiws]

Could this be used to measure volts or currents or ohms ?