Introduction to the unit circle  Trigonometry  Khan Academy  Summary and Q&A
TL;DR
This video explains how to use the unit circle to extend our traditional definitions of trigonometric functions.
Questions & Answers
Q: What is the unit circle and how does it relate to trigonometry?
The unit circle is a circle with a radius of 1 centered at the origin. It helps us visualize coordinates and angles in trigonometry.
Q: How do we determine the coordinates of points on the unit circle?
The xcoordinate of a point on the unit circle is equal to the cosine of the angle, while the ycoordinate is equal to the sine of the angle.
Q: How does the unit circle help us extend the definitions of trigonometric functions?
By using the coordinates of points on the unit circle, we can define cosine as the xcoordinate and sine as the ycoordinate. This allows us to evaluate trigonometric functions for any angle, not just right triangles.
Q: What is the relationship between the unit circle and positive angles?
Positive angles are measured counterclockwise from the positive xaxis. The terminal side of an angle intersects the unit circle at a point whose coordinates represent the values of cosine and sine.
Summary & Key Takeaways

The unit circle is a circle with a radius of 1 and is centered at the origin. It helps us visualize coordinates and angles.

Positive angles are measured counterclockwise from the positive xaxis, while negative angles are measured clockwise.

The sine of an angle is equal to the ycoordinate of the point where the angle intersects the unit circle, and the cosine is equal to the xcoordinate.

By using the unit circle, we can extend the definitions of trigonometric functions beyond right triangles.