How to Find a Cosine Value on the Unit Circle

Step-by-step solution

1. Find the reference angle.

   $$180^\circ - 120^\circ = 60^\circ$$

   Why: The reference angle measures the distance to the x-axis.

2. Use the matching acute value.

   $$\cos 60^\circ = \frac{1}{2}$$

   Why: Cosine of the reference angle gives the size of the answer.

3. Attach the quadrant sign.

   $$\cos 120^\circ = -\frac{1}{2}$$

   Why: An angle between 90 and 180 degrees sits in quadrant II, where cosine is negative.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\cos 150^\circ$

   Show answer

   $-\frac{\sqrt{3}}{2}$

2. 2

   $\cos 135^\circ$

   Show answer

   $-\frac{\sqrt{2}}{2}$

3. 3

   $\cos 180^\circ$

   Show answer

   $-1$

4. 4

   $\cos 90^\circ$

   Show answer

   $0$

5. 5

   $\cos 60^\circ$

   Show answer

   $\frac{1}{2}$