Question

Find the angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}{360}^{\circ }$ that is coterminal with the given angle.

${780}^{\circ }$

Short answer

The Coterminal Angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}{360}^{\circ }$ for${780}^{\circ }$ is ${\mathbf{60}}^{\mathbf{\circ }}$.

Step-by-step solution

Step 1. Given information.

The given angle is:

${780}^{\circ }$.

Step 2. Explanation.

We need to evaluate the value of the Coterminal angle.

To achieve the coterminal angle with ${780}^{\circ }$ we subtract ${360}^{\circ }$ from it.

Step 3. Calculation.

The resulting value of coterminal angle with a given angle $\theta \text{\hspace{0.17em}is\hspace{0.17em}}=\theta -x\left({360}^{\circ }\right)$

Where x is the multiple of ${360}^{\circ }$.

For $\theta ={780}^{\circ },x=2$

Thus,

$$\begin{gathered} \text{Coterminal\hspace{0.17em}Angle}={780}^{\circ }-2\left({360}^{\circ }\right) \\ ={60}^{\circ } \end{gathered}$$

The value of the Coterminal Angle is ${60}^{\circ }$.