Question

convert the angle \frac{11\pi}{4} radians to degrees.

Explanation:

Step1: Use the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
Given \( \text{Radians}=\frac{11\pi}{4}\), then \( \text{Degrees}=\frac{11\pi}{4}\times\frac{180^{\circ}}{\pi}\).

Step2: Simplify the expression

Cancel out the \( \pi\) terms: \( \frac{11\pi}{4}\times\frac{180^{\circ}}{\pi}=\frac{11\times180^{\circ}}{4}\).
Now, calculate \( \frac{11\times180}{4}\). First, \( 180\div4 = 45\), then \( 11\times45=495\).

Answer:

\(495^{\circ}\)