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

To convert degrees to radians, use the formula $radians = degrees\times\frac{\pi}{180}$.

Step2: Substitute the given degree value

Substitute $117$ for degrees in the formula: $117\times\frac{\pi}{180}$.

Step3: Simplify the fraction

Find the greatest - common divisor of 117 and 180. The GCD of 117 and 180 is 9. Divide both the numerator and denominator by 9: $\frac{117\div9}{180\div9}\pi=\frac{13}{20}\pi$.

Answer:

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