Question

convert the following angle from degrees to radians. express your answer in simplest form. 390°

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, use the formula: radians = degrees $\times\frac{\pi}{180}$.

Step2: Substitute the given degree value

For $390^{\circ}$, we have $390\times\frac{\pi}{180}$.

Step3: Simplify the fraction

First, simplify $\frac{390}{180}$.
$390 = 30\times13$ and $180=30\times6$.
So, $\frac{390}{180}=\frac{13}{6}$.
Then $390\times\frac{\pi}{180}=\frac{13\pi}{6}$.

Answer:

$\frac{13\pi}{6}$ radians