Question

convert the angle $\frac{5\pi}{4}$ radians to degrees.

Explanation:

Step1: Use the conversion formula

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).
For the angle \(\frac{5\pi}{4}\) radians, substitute into the formula: \(\frac{5\pi}{4}\times\frac{180^{\circ}}{\pi}\).

Step2: Simplify the expression

The \(\pi\) terms cancel out. Then calculate \(\frac{5\times180^{\circ}}{4}\).
\(5\times45^{\circ}=225^{\circ}\) (since \(\frac{180}{4} = 45\)).

Answer:

225