Question

convert the following angle from degrees to radians. express your answer in simplest form.
420°

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

Substitute $420^{\circ}$ into the formula: $420\times\frac{\pi}{180}$.

Step3: Simplify the fraction

Simplify $\frac{420}{180}$. Divide numerator and denominator by $60$: $\frac{420\div60}{180\div60}=\frac{7}{3}$. So, $420\times\frac{\pi}{180}=\frac{7\pi}{3}$.

Answer:

$\frac{7\pi}{3}$