Question

convert the following angle from degrees to radians. express your answer in simplest form. 555° answer submit answer π

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180}\).
For \(555^{\circ}\), we have \(555\times\frac{\pi}{180}\).

Step2: Simplify the fraction

First, find the greatest - common divisor (GCD) of 555 and 180.
Prime factorize: \(555 = 3\times5\times37\), \(180=2^{2}\times3^{2}\times5\).
The GCD of 555 and 180 is \(15\).
Divide numerator and denominator by 15: \(\frac{555\div15}{180\div15}\times\pi=\frac{37}{12}\pi\).

Answer:

\(\frac{37\pi}{12}\)