Question

given the reference angle of \\(\frac{\pi}{5}\\), find the corresponding angle in quadrant 4.

Explanation:

Step1: Recall Quadrant 4 angle formula

In Quadrant 4, the angle \(\theta\) (in radians) is given by \(2\pi - \text{reference angle}\) when the reference angle is measured from the positive x - axis.

Step2: Substitute the reference angle

The reference angle is \(\frac{\pi}{5}\). So we calculate \(2\pi-\frac{\pi}{5}\). First, find a common denominator, which is 5. Then \(2\pi=\frac{10\pi}{5}\). So \(\frac{10\pi}{5}-\frac{\pi}{5}=\frac{10\pi - \pi}{5}=\frac{9\pi}{5}\).

Answer:

\(\frac{9\pi}{5}\)