Question

convert the angle in radians to degrees. \\(\frac{31\pi}{18}\\) radians \\(\frac{31\pi}{18}\\) radians = \\(\square^{\circ}\\)

Explanation:

Step1: Recall radian to degree formula

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

Step2: Substitute the given radian value

We have the radian measure \( \frac{31\pi}{18} \). Substitute this into the formula:
\( \frac{31\pi}{18} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out. Then, simplify \( \frac{180}{18} = 10 \). So we have \( 31\times10^\circ = 310^\circ \)

Answer:

\( 310 \)