Question

convert the angle θ = \frac{5π}{12} radians to degrees. express your answer exactly. θ = \boxed{ } ^\circ

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given radian measure

We have \( \theta = \frac{5\pi}{12} \) radians. Substitute this into the formula:
\( \theta = \frac{5\pi}{12} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \theta = \frac{5}{12} \times 180^\circ \)
Calculate \( \frac{5 \times 180}{12} \):
First, \( 180 \div 12 = 15 \), then \( 5 \times 15 = 75 \)

Answer:

\( 75 \)