Question

convert the angle θ = \frac{133π}{72} radians to degrees. express your answer exactly. θ = \boxed{\space}°

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 are given \( \theta = \frac{133\pi}{72} \) radians. Substitute this into the formula:
\( \theta = \frac{133\pi}{72} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \theta = \frac{133 \times 180^\circ}{72} \)

Simplify \( \frac{180}{72} = \frac{5}{2} \), so:
\( \theta = 133 \times \frac{5}{2}^\circ \)

Calculate \( 133 \times 5 = 665 \), then divide by 2:
\( \theta = \frac{665}{2}^\circ = 332.5^\circ \)

Answer:

\( 332.5^\circ \) (or \( \frac{665}{2}^\circ \))