Question

convert the following angle from degrees to radians. express your answer in simplest form. 165°

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, we use the formula: $radians = degrees\times\frac{\pi}{180}$.
For $165^{\circ}$, we have $165\times\frac{\pi}{180}$.

Step2: Simplify the fraction

First, find the greatest common divisor (GCD) of 165 and 180.
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
The GCD of 165 and 180 is 15.
Divide both the numerator and denominator by 15: $\frac{165\div15}{180\div15}\times\pi=\frac{11}{12}\pi$.

Answer:

$\frac{11\pi}{12}$