Question

rewrite each angle in degree measure. (do not use a calculator.) (a) $\frac{3pi}{2}$ (b) $\frac{7pi}{6}$ resources

Explanation:

Step1: Recall conversion formula

We know that $\pi$ radians $ = 180^{\circ}$. So to convert radians to degrees, we use the formula $D=R\times\frac{180^{\circ}}{\pi}$, where $D$ is the degree - measure and $R$ is the radian - measure.

Step2: Convert $\frac{3\pi}{2}$ to degrees

Substitute $R = \frac{3\pi}{2}$ into the formula: $D=\frac{3\pi}{2}\times\frac{180^{\circ}}{\pi}$. The $\pi$ terms cancel out, and $\frac{3}{2}\times180^{\circ}=3\times90^{\circ}=270^{\circ}$.

Step3: Convert $\frac{7\pi}{6}$ to degrees

Substitute $R=\frac{7\pi}{6}$ into the formula: $D = \frac{7\pi}{6}\times\frac{180^{\circ}}{\pi}$. The $\pi$ terms cancel out, and $\frac{7}{6}\times180^{\circ}=7\times30^{\circ}=210^{\circ}$.

Answer:

(a) $270^{\circ}$
(b) $210^{\circ}$