Question

convert the following angle in degrees to radians. 117° 117° = radians (simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall conversion formula

We know that to convert degrees to radians, we use the formula $x^{\circ}=x\times\frac{\pi}{180}$ radians.

Step2: Substitute the given value

For $x = 117$, we have $117^{\circ}=117\times\frac{\pi}{180}$ radians.

Step3: Simplify the fraction

$\frac{117}{180}=\frac{13\times9}{20\times9}=\frac{13}{20}$. So $117^{\circ}=\frac{13\pi}{20}$ radians.

Answer:

$\frac{13\pi}{20}$