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.

$-{800}^{\circ }$

Short answer

The Coterminal Angle between$0^{\circ }\text{\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}{360}^{\circ }$ for$-{800}^{\circ }$ is ${\mathbf{280}}^{\mathbf{\circ }}$.

Step-by-step solution

Step 1. Given information.

The given angle is:

$-{800}^{\circ }$.

Step 2. Explanation.

We need to evaluate the value of the Coterminal angle.

To achieve the coterminal angle with$-{800}^{\circ }$ 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$\theta =-{800}^{\circ },x=2$

Thus,

role="math" localid="1648716545268" $\begin{array}{l}\text{Coterminal\hspace{0.17em}Angle}=-{800}^{\circ }+2\left({360}^{\circ }\right)\\ =-{80}^{\circ }\\ \text{Coterminal\hspace{0.17em}Angle}=-{80}^{\circ }+{360}^{\circ }\\ ={280}^{\circ }\end{array}$

The value of the Coterminal Angle is ${280}^{\circ }$.