Solution

Convert to degrees: $\displaystyle{\frac{7\pi}{6}}$ radians, $\displaystyle{-\frac{\pi}{12}}$ radians, $0.76$ radians


Each case is treated in the same way. Since $\pi \textrm{ radians } = 180^{\circ}$, we multiply angle measures in radians by $180^{\circ} \, / \, \pi$ to convert them to angle measures in degrees:

  • $\displaystyle{\frac{7\pi}{6} \textrm{ radians } = \frac{7\pi}{6} \cdot \left( \frac{180^{\circ}}{\pi} \right) = 210^{\circ}}$

  • $\displaystyle{-\frac{\pi}{12} \textrm{ radians } = -\frac{\pi}{12} \cdot \left( \frac{180^{\circ}}{\pi} \right) = -15^{\circ}}$

  • $\displaystyle{0.76 \textrm{ radians } = 0.76 \cdot \left( \frac{180^{\circ}}{\pi} \right) = \left( \frac{136.8}{\pi} \right)^{\circ} \approx 48.54^{\circ}}$