Questions: Convert 340 degrees to radians radians Convert 31 pi/18 to degrees degrees

Solution Steps

To convert degrees to radians, use the formula: \[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \] Substitute 340 degrees into the formula: \[ 340^\circ \times \left( \frac{\pi}{180} \right) = \frac{340\pi}{180} \] Simplify the fraction: \[ \frac{340\pi}{180} = \frac{17\pi}{9} \]

To convert radians to degrees, use the formula: \[ \text{degrees} = \text{radians} \times \left( \frac{180}{\pi} \right) \] Substitute \(\frac{31\pi}{18}\) into the formula: \[ \frac{31\pi}{18} \times \left( \frac{180}{\pi} \right) = \frac{31 \times 180}{18} \] Simplify the expression: \[ \frac{31 \times 180}{18} = 31 \times 10 = 310^\circ \]

The exact answers are: \[ 340^\circ = \frac{17\pi}{9} \text{ radians} \] \[ \frac{31\pi}{18} = 310^\circ \]

Final Answer