Question

given the reference angle of \\(\frac{2\pi}{7}\\), find the corresponding angle in quadrant 3.

Explanation:

Step1: Recall Quadrant 3 angle formula

In Quadrant 3, the angle \(\theta\) is given by \(\pi + \text{reference angle}\).

Step2: Substitute reference angle

The reference angle is \(\frac{2\pi}{7}\), so the angle in Quadrant 3 is \(\pi+\frac{2\pi}{7}\).

Step3: Simplify the expression

Find a common denominator: \(\pi=\frac{7\pi}{7}\), so \(\frac{7\pi}{7}+\frac{2\pi}{7}=\frac{9\pi}{7}\).

Answer:

\(\frac{9\pi}{7}\)