Question

convert the following angle from degrees to radians. express your answer in simplest form.
480°

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, use the formula: \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180}\)
So for \(480^{\circ}\), we have \(480\times\frac{\pi}{180}\)

Step2: Simplify the fraction

\(480\times\frac{\pi}{180}=\frac{480\pi}{180}\)
Divide numerator and denominator by \(60\): \(\frac{480\div60}{180\div60}\pi=\frac{8}{3}\pi\)

Answer:

\(\frac{8}{3}\pi\) radians