which angle is coterminal with $-\frac{4pi}{3}$? $\frac{8pi}{3}$ $-\frac{11pi}{3}$ $\frac{5pi}{3}$

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for coterminal angles
Coterminal angles are given by $\theta + 2k\pi$, where $k\in\mathbb{Z}$. Here $\theta=-\frac{4\pi}{3}$.
## Step2: Substitute $k = 1$ into the formula
$$
\begin{align*}
-\frac{4\pi}{3}+2\pi&=-\frac{4\pi}{3}+\frac{6\pi}{3}\
&=\frac{- 4\pi + 6\pi}{3}\
&=\frac{2\pi}{3}
\end{align*}
$$
## Step3: Substitute $k = 2$ into the formula
$$
\begin{align*}
-\frac{4\pi}{3}+4\pi&=-\frac{4\pi}{3}+\frac{12\pi}{3}\
&=\frac{-4\pi + 12\pi}{3}\
&=\frac{8\pi}{3}
\end{align*}
$$

# Answer:
$\frac{8\pi}{3}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for coterminal angles

Step2: Substitute \(k = 1\) into the formula

Step3: Substitute \(k = 2\) into the formula

Answer: