Question

what is the equivalent degree measure of $\frac{5pi}{3}$ radians written in simplest terms? $\frac{7pi}{360}$, 108., 300., $\frac{pi}{5}$

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the degree - measure and $R$ is the radian - measure.

Step2: Substitute the given value

Given $R=\frac{5\pi}{3}$. Substitute it into the formula: $D=\frac{5\pi}{3}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out, and $\frac{180}{3}=60$. Then $5\times60 = 300^{\circ}$.

Answer:

$300^{\circ}$