﻿ Graph and Formula for the Unit Circle as a function of Sine and Cosine

# Unit Circle Formula

Demonstration of the Unit Circle Formula & Graph

### Graphs of Sine/Cosine From Unit Circlle

The Unit Circle is a circle with a radius of 1. The angle that we rotate the radius uses the greek letter θ.

### Formula for the Unit Circle

The formula for the unit circle relates the coordinates of any point on the unit circle to sine and cosine. According to the formula, the x coordinate of a point on the unit circle is $$cos (\theta)$$ and the y coordinate of a point on the unit circle is $$sin(\theta)$$ where Θ represents the measure of an angle that goes counter clockwise from the positive x-axis. This formula is much easier to see and understand from a picture. See the first problem below.

### Practice Problems

##### Problem 2

The value of the x coordinate is the $$cos(\theta)$$ and the y coordinate is $$sin(\theta)$$.

##### Problem 3

Remember the formula for the unit circle. Cosine represents the x value, segment AB, sine represents the y value or CB and the tangent line rests outside the circle and is DF.

##### Problem 4

Remember the formula for the unit circle. Cosine represents the x value, segment AB, sine represents the y value or CB and the tangent line rests outside the circle and is DF.

##### Problem 5

Remember the formula for the unit circle. Cosine represents the x value, segment PL, sine represents the y value or PO and the tangent line rests outside the circle and is NM.

##### Problem 6

Remember the formula for the unit circle. Cosine represents the x value, segment AE, sine represents the y value or ED and the tangent line rests outside the circle and is BC.

##### Problem 7

Remember the formula for the unit circle. Cosine represents the x value, segment OS, sine represents the y value or SQ and the tangent line rests outside the circle and is PR.