Question

convert the following angle from degrees to radians. express your answer in simplest form.
105°

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 \( 105^\circ \), so substitute into the formula: \( 105 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

First, find the greatest common divisor (GCD) of 105 and 180. The GCD of 105 and 180 is 15. Divide both the numerator and the denominator by 15: \( \frac{105 \div 15}{180 \div 15} \times \pi = \frac{7}{12}\pi \)

Answer:

\( \frac{7}{12}\pi \)