Question

convert the angle θ = \frac{3π}{5} radians to degrees. express your answer exactly. θ = \boxed{ }°

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 \( \theta = \frac{3\pi}{5} \) radians. Substitute this into the formula:
\( \theta = \frac{3\pi}{5} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) in the numerator and denominator cancels out:
\( \theta = \frac{3}{5} \times 180^\circ \)
Calculate \( \frac{3 \times 180^\circ}{5} \):
\( 3 \times 36^\circ = 108^\circ \)

Answer:

\( 108 \)