Question

consider the following angle, measured in radians: $x = \frac{7\pi}{6}$. what is the measure of the angle in degrees?

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula $y=x\times\frac{180^{\circ}}{\pi}$, where $x$ is the angle in radians and $y$ is the angle in degrees.

Step2: Substitute the given value

Substitute $x = \frac{7\pi}{6}$ into the formula: $y=\frac{7\pi}{6}\times\frac{180^{\circ}}{\pi}$.

Step3: Simplify the expression

The $\pi$ terms cancel out, and $\frac{180}{6}=30$. Then $7\times30 = 210$. So $y = 210^{\circ}$.

Answer:

$210^{\circ}$