Question

convert the angle θ = \\(\frac{29\pi}{15}\\) radians to degrees. express your answer exactly. \\(\theta = \square^\circ\\) show calculator.

Explanation:

Step1: Recall radian to degree 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 \( \theta = \frac{29\pi}{15} \) radians. Substitute this into the formula:
\( \theta = \frac{29\pi}{15} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out:
\( \theta = \frac{29}{15} \times 180^\circ \)
Calculate \( \frac{180}{15} = 12 \), then multiply by 29:
\( \theta = 29 \times 12^\circ = 348^\circ \)

Answer:

\( 348 \)