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 the conversion formula

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

Step2: Substitute the given degree value

We are given \( 117^\circ \), so substitute into the formula:
\( 117^\circ \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{117}{180} \) by finding the greatest common divisor (GCD) of 117 and 180, which is 9. Divide numerator and denominator by 9:
\( \frac{117 \div 9}{180 \div 9} = \frac{13}{20} \)

So, \( 117^\circ = \frac{13}{20}\pi \) radians

Answer:

\(\frac{13}{20}\pi\)