Question

question
convert the angle $\frac{11\pi}{12}$ radians to degrees.
answer
attempt 1 out of 5

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given value

Given \( \text{Radians}=\frac{11\pi}{12}\), then \( \text{Degrees}=\frac{11\pi}{12}\times\frac{180^{\circ}}{\pi}\).

Step3: Simplify the expression

The \( \pi\) terms cancel out. \( \frac{11}{12}\times180^{\circ}=11\times15^{\circ}=165^{\circ}\).

Answer:

165^{\circ}