Question

which angle is coterminal with \frac{5pi}{6}? -\frac{pi}{6} -\frac{7pi}{6} -\frac{11pi}{6}

Explanation:

Step1: Recall the formula for coterminal angles

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

Step2: Check each option

• For $-\frac{\pi}{6}$:

$$\frac{5\pi}{6}+2k\pi=-\frac{\pi}{6}$$
$$2k\pi=-\frac{\pi}{6}-\frac{5\pi}{6}=- \pi$$

$$k =-\frac{1}{2} otin\mathbb{Z}$$

• For $-\frac{7\pi}{6}$:

$$\frac{5\pi}{6}+2k\pi=-\frac{7\pi}{6}$$
$$2k\pi=-\frac{7\pi}{6}-\frac{5\pi}{6}=- 2\pi$$
$$k=-1\in\mathbb{Z}$$

• For $-\frac{11\pi}{6}$:

$$\frac{5\pi}{6}+2k\pi=-\frac{11\pi}{6}$$
$$2k\pi=-\frac{11\pi}{6}-\frac{5\pi}{6}=- \frac{16\pi}{6}=-\frac{8\pi}{3}$$

$$k =-\frac{4}{3} otin\mathbb{Z}$$

Answer:

$-\frac{7\pi}{6}$