Question

convert the following angle from degrees to radians. express your answer in simplest form.
690°

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given angle

We have the angle \( 690^\circ \). Substitute it into the formula:
\( 690 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 690 and 180. The GCD of 690 and 180 is 30.
Divide both the numerator and the denominator by 30:
\( \frac{690 \div 30}{180 \div 30} \times \pi = \frac{23}{6} \pi \)

Answer:

\( \frac{23}{6}\pi \)