Question

1. $\frac{\pi}{5}$ radians = ______ degrees
2. $\frac{5\pi}{6}$ radians = ______ degrees

Explanation:

Step1: Recall the conversion formula

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

Step2: Solve for \( \frac{\pi}{5}\) radians

Substitute \( \text{Radians}=\frac{\pi}{5}\) into the formula:
\( \text{Degrees}=\frac{\pi}{5}\times\frac{180^{\circ}}{\pi}\)
Cancel out \( \pi\): \( \frac{180^{\circ}}{5} = 36^{\circ}\)

Step3: Solve for \( \frac{5\pi}{6}\) radians

Substitute \( \text{Radians}=\frac{5\pi}{6}\) into the formula:
\( \text{Degrees}=\frac{5\pi}{6}\times\frac{180^{\circ}}{\pi}\)
Cancel out \( \pi\): \( \frac{5\times180^{\circ}}{6}\)
\( 5\times30^{\circ}=150^{\circ}\)

Answer:

1. \( 36\)
2. \( 150\)