Question

convert 150° to radians. a. \\(\frac{5\pi}{6}\\) radians b. \\(\frac{6\pi}{5}\\) radians c. \\(\frac{3\pi}{4}\\) radians d. \\(\frac{2\pi}{3}\\) radians

Explanation:

Step1: Recall degree - radian conversion formula

The formula to convert degrees to radians is: \( \text{radians}=\text{degrees}\times\frac{\pi}{180} \)

Step2: Substitute the given degree value

We are given \( 150^{\circ} \), so substitute \( \text{degrees} = 150 \) into the formula:
\( 150\times\frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{150}{180} \). Both numerator and denominator are divisible by 30. \( \frac{150\div30}{180\div30}=\frac{5}{6} \). So \( 150\times\frac{\pi}{180}=\frac{5\pi}{6} \) radians.

Answer:

A. \( \frac{5\pi}{6} \) radians