Question

convert \frac{7\pi}{12} radians to degrees. 12 of 12 question 0.032° 210° 105° 52.5°

Explanation:

Step1: Use the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
Given \( \text{Radians}=\frac{7\pi}{12}\), then \( \text{Degrees}=\frac{7\pi}{12}\times\frac{180^{\circ}}{\pi}\).

Step2: Simplify the expression

Cancel out the \( \pi\) terms: \( \frac{7}{12}\times180^{\circ}\).
Calculate \( \frac{7\times180^{\circ}}{12}\).
Since \( 180\div12 = 15\), then \( 7\times15^{\circ}=105^{\circ}\).

Answer:

\(105^{\circ}\) (corresponding to the third option in the multiple - choice list)