Question

1. given the reference angle of \\(\frac{\pi}{10}\\), find the corresponding angle in quadrant 3.

Explanation:

Step1: Recall Quadrant 3 angle formula

For an angle in Quadrant 3, the angle \(\theta\) is given by \(\theta=\pi + \text{reference angle}\).

Step2: Substitute reference angle

The reference angle is \(\frac{\pi}{10}\), so we substitute into the formula: \(\theta=\pi+\frac{\pi}{10}\).

Step3: Simplify the expression

To add \(\pi\) (which is \(\frac{10\pi}{10}\)) and \(\frac{\pi}{10}\), we get \(\frac{10\pi}{10}+\frac{\pi}{10}=\frac{11\pi}{10}\).

Answer:

\(\frac{11\pi}{10}\)