Question

convert 72 degrees to radians. (1 point)
(\frac{2pi}{5}) radians
(\frac{pi}{5}) radians
(\frac{2pi}{4}) radians
(\frac{3pi}{2}) radians

Explanation:

Step1: Recall degree to radian formula

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

Step2: Substitute 72 degrees into the formula

Substitute \( 72^\circ \) into the formula: \( 72 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{72}{180} \). We can divide numerator and denominator by 36: \( \frac{72\div36}{180\div36}=\frac{2}{5} \). So the result is \( \frac{2\pi}{5} \) radians.

Answer:

\( \frac{2\pi}{5} \) radians (corresponding to the first option: \( \boldsymbol{\frac{2\pi}{5}} \) radians)