Question

find the measures of two angles, one positive and one negative, that are coterminal with the given angle. show work. 14) $\frac{8\pi}{5}$ a) $\frac{2\pi}{5}; -\frac{18\pi}{5}$ b) $\frac{13\pi}{5}; -\frac{2\pi}{5}$ c) $\frac{18\pi}{5}; -\frac{2\pi}{5}$ d) $\frac{13\pi}{5};$

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by \(\theta + 2k\pi\), where \(k\in\mathbb{Z}\).

Step2: Find a positive coterminal angle

Let \(k = 1\). Then \(\frac{8\pi}{5}+2\pi=\frac{8\pi}{5}+\frac{10\pi}{5}=\frac{18\pi}{5}\).

Step3: Find a negative coterminal angle

Let \(k=-1\). Then \(\frac{8\pi}{5}-2\pi=\frac{8\pi}{5}-\frac{10\pi}{5}=-\frac{2\pi}{5}\).

Answer:

C. \(\frac{18\pi}{5};-\frac{2\pi}{5}\)