Question

Find the angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}2\pi$ that is coterminal with the given angle.

$-\frac{5\pi }{3}$

Short answer

The Coterminal Angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}2\pi$ for$-\frac{5\pi }{3}$ is $\frac{\mathbf{\pi }}{\mathbf{3}}$.

Step-by-step solution

Step 1. Given information.

The given angle is:

$-\frac{5\pi }{3}$.

Step 2. Explanation.

We need to evaluate the value of the Coterminal angle.

To achieve the coterminal angle with $-\frac{5\pi }{3}$ we subtract $2\pi$ from it.

Step 3. Calculation.

The resulting value of coterminal angle with a given angle$\theta \text{\hspace{0.17em}is\hspace{0.17em}}=\theta +x\left(2\pi \right)$

Where $x$is the multiple of $2\pi$.

For$\theta =-\frac{5\pi }{3},x=1$

Thus,

$$\begin{gathered} \text{Coterminal\hspace{0.17em}Angle}=-\frac{5\pi }{3}+1\left(2\pi \right) \\ =\frac{\pi }{3} \end{gathered}$$

The value of the Coterminal Angle is $\frac{\pi }{3}$.