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, use the formula: radians = degrees $\times\frac{\pi}{180}$.
So, for $165^{\circ}$, we have $165\times\frac{\pi}{180}$.

Step2: Simplify the fraction

Simplify $\frac{165}{180}$. The greatest common divisor of 165 and 180 is 15.
$\frac{165\div15}{180\div15}=\frac{11}{12}$.
So, $165\times\frac{\pi}{180}=\frac{11\pi}{12}$.

Answer:

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