Question

convert the angle $\theta = 310^\circ$ to radians. express your answer exactly. $\theta = \square$ radians

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 \( \theta = 310^\circ \), so substitute into the formula: \( 310 \times \frac{\pi}{180} \).

Step3: Simplify the fraction

Simplify \( \frac{310}{180} \) by dividing numerator and denominator by 10: \( \frac{31}{18} \). So the angle in radians is \( \frac{31\pi}{18} \).

Answer:

\( \frac{31\pi}{18} \)