Question

question find the reference angle for a rotation of 4π/3. answer attempt 1 out of 3

Explanation:

Step1: Determine the quadrant

Since \(\frac{4\pi}{3}\) is between \(\pi\) and \(\frac{3\pi}{2}\), it lies in the third quadrant.

Step2: Calculate the reference angle

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

Answer:

\(\frac{\pi}{3}\)