Question

convert the angle in radians to degrees.
\frac{7\pi}{6} radians
\frac{7\pi}{6} radians = \square^\circ

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given radian measure

We have \( \frac{7\pi}{6} \) radians. Substitute this into the formula:
\( \frac{7\pi}{6} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \frac{7}{6} \times 180^\circ \)
Calculate \( \frac{7 \times 180^\circ}{6} \). First, \( 180 \div 6 = 30 \), then \( 7 \times 30^\circ = 210^\circ \)

Answer:

\( 210 \)