Question

convert the following angle from degrees to radians. express your answer in simplest form. 615°

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, use the formula: radians = degrees $\times\frac{\pi}{180}$.
So for $615^{\circ}$, we have $615\times\frac{\pi}{180}$.

Step2: Simplify the fraction

First, find the greatest common divisor (GCD) of 615 and 180.
The prime factorization of 615 is $3\times5\times41$, and of 180 is $2^{2}\times3^{2}\times5$.
The GCD of 615 and 180 is 15.
Divide both numerator and denominator by 15: $\frac{615\div15}{180\div15}\times\pi=\frac{41}{12}\pi$.

Answer:

$\frac{41\pi}{12}$