Question

radian measure
introduction to radian measure
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convert the angle \\( \frac { 5 \pi } { 4 } \\) from radians to degrees.
degrees
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Explanation:

Step1: Recall the conversion formula

The formula to convert radians to degrees is \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}\).

Step2: Substitute the given value

Substitute \( \text{Radians}=\frac{5\pi}{4}\) into the formula: \( \text{Degrees}=\frac{5\pi}{4}\times\frac{180^{\circ}}{\pi}\).

Step3: Simplify the expression

Cancel out the \(\pi\) terms: \( \text{Degrees}=\frac{5}{4}\times180^{\circ}\). Then calculate \( \frac{5\times180^{\circ}}{4}= 225^{\circ}\).

Answer:

\(225\)