1. Convert degrees to radians. (a) Convert 300° to radians. Recall the formula: $$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$ $$300^\circ = 300 \times \frac{\pi}{180} = \frac{300\pi}{180} = \frac{5\pi}{3}$$ So, 300° equals $$\frac{5\pi}{3}$$ radians. (b) Convert -18° to radians. $$-18^\circ = -18 \times \frac{\pi}{180} = \frac{-18\pi}{180} = \frac{-\pi}{10}$$ So, -18° equals $$-\frac{\pi}{10}$$ radians. 2. Convert radians to degrees. Use the formula: $$\text{degrees} = \text{radians} \times \frac{180}{\pi}$$ (a) Convert $$\frac{5\pi}{6}$$ radians to degrees. $$\frac{5\pi}{6} \times \frac{180}{\pi} = \frac{5 \times 180}{6} = 150^\circ$$ So, $$\frac{5\pi}{6}$$ radians equals 150°. (b) Convert 2 radians to degrees. $$2 \times \frac{180}{\pi} = \frac{360}{\pi} \approx 114.59^\circ$$ So, 2 radians is approximately 114.59°. Summary of conversions: - 300° = $$\frac{5\pi}{3}$$ radians - -18° = $$-\frac{\pi}{10}$$ radians - $$\frac{5\pi}{6}$$ radians = 150° - 2 radians ≈ 114.59° Each step used standard conversion formulas between degrees and radians, multiplying by $$\frac{\pi}{180}$$ to convert degrees to radians, and $$\frac{180}{\pi}$$ to convert radians to degrees. Understanding these conversions helps us interpret the angles in the described geometric contexts like triangles, circles, and unit circle measures.