Unit Circle

Definition: The unit circle is a circle whose center is (0,0) with a radius of 1 unit. It can be used to determine values of trigonometric functions at specific angles.

The coordinates of the  endpoints on the unit circle are given as (cos, sin).

Example 1: Use the unit circle to determine cos 150°

Solution

Step 1: Find 150° on the unit circle and observe the corresponding coordinates

Step 2: Keeping in mind that endpoints on the unit circle are given as (cos, sin), the x-value of this point will indicate cos 150°:

Example 2: Use the unit circle to determine sin(5π/3)

Step 1: Find 5π/3 on the unit circle and observe the corresponding coordinates:$\bg_white \large \left (\frac{\;1\;}{2},\frac{\mbox{-}\sqrt{3}}{2} \right )$

Step 2: Keeping in mind that endpoints on the unit circle are given as (cos, sin), the y-value of this point will indicate sin(5π/3):

$\dpi{120} \bg_white \large \textup{sin}\, \frac{5\pi}{3}\;= \;-\frac{\sqrt{3}}{2}$

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