Question

given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.
cos 120°

Explanation:

Step1: Find the reference angle

The angle \(120^{\circ}\) is in the second quadrant. The formula for the reference angle \(\theta_{r}\) in the second quadrant is \(\theta_{r}=180^{\circ}-\theta\).
So, \(\theta_{r}=180^{\circ} - 120^{\circ}=60^{\circ}\)

Step2: Determine the sign of the cosine function

In the second quadrant, the \(x\) - coordinate (since \(\cos\theta=x\) on the unit circle) is negative.

Step3: Use the cosine of the reference angle

We know that \(\cos60^{\circ}=\frac{1}{2}\). Since \(\cos120^{\circ}\) is negative in the second quadrant, \(\cos120^{\circ}=-\cos60^{\circ}\)

Answer:

\(-\frac{1}{2}\)