Question

find the exact value.
cos\frac{4\pi}{3}
type + or -
? \frac{}{}

Explanation:

Step1: Determine the reference angle

The angle \(\frac{4\pi}{3}\) is in the third quadrant. The reference angle \(\theta_{r}\) for an angle \(\theta=\frac{4\pi}{3}\) is \(\theta_{r}=\frac{4\pi}{3}-\pi=\frac{\pi}{3}\).

Step2: Use the cosine value of the reference angle and the sign in the third quadrant

We know that \(\cos\frac{\pi}{3}=\frac{1}{2}\). In the third quadrant, \(\cos\theta<0\). So \(\cos\frac{4\pi}{3}=-\cos\frac{\pi}{3}\).

Answer:

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