Question

convert the angle in degrees to radians. express your answer as a multiple of π.
120°
120° = radians
(simplify your answer. use integer or fractions for any numbers in the expression.)

Explanation:

Step1: Recall degree - radian conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180}\).

Step2: Substitute the given degree value

Given \(120^{\circ}\), substitute into the formula: \(120\times\frac{\pi}{180}\).

Step3: Simplify the fraction

Simplify \(\frac{120}{180}\). Divide numerator and denominator by 60. \(\frac{120\div60}{180\div60}=\frac{2}{3}\). So \(120\times\frac{\pi}{180}=\frac{2\pi}{3}\).

Answer:

\(\frac{2\pi}{3}\) radians