Question

convert the angle $\theta=\frac{29pi}{15}$ radians to degrees. express your answer exactly. $\theta=square^{circ}$

Explanation:

Step1: Recall conversion formula

To convert radians to degrees, use the formula $1$ radian $=\frac{180^{\circ}}{\pi}$. So if $\theta$ is in radians, to convert to degrees we multiply by $\frac{180^{\circ}}{\pi}$.

Step2: Apply the formula

Given $\theta=\frac{29\pi}{15}$ radians. Multiply by $\frac{180^{\circ}}{\pi}$: $\theta=\frac{29\pi}{15}\times\frac{180^{\circ}}{\pi}$.
The $\pi$ terms cancel out. Then we have $\frac{29\times180^{\circ}}{15}$.

Step3: Simplify the expression

$180\div15 = 12$, so $29\times12^{\circ}=348^{\circ}$.

Answer:

$348$