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, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180^\circ} \)

Step2: Substitute the given angle

We have the angle \( 480^\circ \). Substitute it into the formula:
\( 480^\circ \times \frac{\pi}{180^\circ} \)

Step3: Simplify the fraction

First, we can simplify the fraction \( \frac{480}{180} \). Both numerator and denominator are divisible by 60:
\( \frac{480 \div 60}{180 \div 60} = \frac{8}{3} \)
So, \( 480^\circ \times \frac{\pi}{180^\circ} = \frac{8\pi}{3} \)

Answer:

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