Question

watch the video and then solve the problem given below. click here to watch the video. convert the angle in radians to degrees. $\frac{5pi}{3}$ radians $\frac{5pi}{3}$ radians = $square^{circ}$ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).

Step2: Substitute the given value

Given \(\text{Radians}=\frac{5\pi}{3}\), then \(\text{Degrees}=\frac{5\pi}{3}\times\frac{180^{\circ}}{\pi}\).

Step3: Simplify the expression

\(\frac{5\pi}{3}\times\frac{180^{\circ}}{\pi}=\frac{5\times180^{\circ}}{3}\). Since \(180\div3 = 60\), then \(5\times60^{\circ}=300^{\circ}\).

Answer:

\(300\)