Question

Find the angle between${\mathbf{0}}^{\mathbf{\circ }}$ and$\mathbf{2}\mathit{\pi }$ that is coterminal with the given angle.

$\frac{\mathbf{51}\mathbf{\pi }}{\mathbf{2}}$

Short answer

The Coterminal Angle between$0^{\circ }$ and$2\pi$ for$\frac{51\pi }{2}$ is$\frac{\mathbf{3}\mathbf{\pi }}{\mathbf{2}}$.

Step-by-step solution

Step 1. Given information

The given angle is:

$\frac{51\pi }{2}$.

Step 2. Explanation

We need to evaluate the value of the Coterminal angle.

To achieve the coterminal angle with$\frac{51\pi }{2}$ we subtract$2\pi$ from it.

Step 3. Calculation

The resulting value of coterminal angle with 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 $\theta =\frac{51\pi }{2},x=12$

Thus,

$\begin{array}{l}\text{Coterminal\hspace{0.17em}Angle}=\frac{51\pi }{2}-12\left(2\pi \right)\\ =\frac{3\pi }{2}\end{array}$

The value of Coterminal Angle is $\frac{3\pi }{2}$.