Question 4.1.3: Converting from Radians to Degrees Convert each angle in rad...

To convert radians to degrees, multiply by \frac{180^{\circ}}{\pi \text { radians }}. Observe how the radian units cancel.

a. \frac{\pi}{3} \text { radians }=\frac{\cancel{\pi}  \cancel{radians }}{3} \cdot \frac{180^{\circ}}{\cancel{\pi}  \cancel{radians}}=\frac{180^{\circ}}{3}=60^{\circ}

b. -\frac{5 \pi}{3}  \text { radians }=-\frac{5 \cancel{\pi}  \cancel{radians }}{3} \cdot \frac{180^{\circ}}{\cancel{\pi}  \cancel{radians}}=-\frac{5 \cdot 180^{\circ}}{3}=-300^{\circ}

c. 1 \text { radian }=1  \cancel{radian } \cdot \frac{180^{\circ}}{\pi  \cancel{radians }}=\frac{180^{\circ}}{\pi}  \approx 57.3^{\circ}

d. 2.3  \text { radians }=2.3  \cancel{ radians } \cdot \frac{180^{\circ}}{\pi  \cancel{ radians }}=\frac{2.3 \cdot 180^{\circ}}{\pi} \approx 131.8^{\circ}