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.

$25\pi$

Short answer

The Coterminal Angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}2\pi$ for$25\mathrm{\pi }$ is $\pi$.

Step-by-step solution

Step 1. Given information.

The given angle is:

$25\pi$.

Step 2. Explanation.

We need to evaluate the value of the Coterminal angle.

To achieve the coterminal angle with $25\pi$ 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$\theta =25\pi ,x=12$

Thus,

$$\begin{gathered} \text{Coterminal\hspace{0.17em}Angle}=25\pi -12\left(2\pi \right) \\ =\pi \end{gathered}$$

The value of the Coterminal Angle is $\pi$.