Question

question
convert the following angle from degrees to radians. express your answer in simplest form.
630°
answer

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180^\circ} \)

Step2: Substitute the given angle

We have the angle \( 630^\circ \). Substitute this into the formula:
\( 630^\circ \times \frac{\pi}{180^\circ} \)

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 630 and 180. The GCD of 630 and 180 is 90.
Divide both the numerator and the denominator by 90:
\( \frac{630 \div 90}{180 \div 90} = \frac{7}{2} \)
So, \( 630^\circ \times \frac{\pi}{180^\circ} = \frac{7\pi}{2} \)

Answer:

\( \frac{7\pi}{2} \)