Question: (\[ \frac{13\pi}{15} \text{ radians} = \underline{\hspace{1cm}} \text{ degrees} \]…

\(\[ \frac{13\pi}{15} \text{ radians} = \underline{\hspace{1cm}} \text{ degrees} \]

Options:

• 78
• 13
• 156
• 195
• 312\)

Solution

To convert radians to degrees, use the formula: \[ \text{degrees} = \text{radians} \times \frac{180}{\pi} \] Substitute \(\frac{13\pi}{15}\) for radians: \[ \text{degrees} = \frac{13\pi}{15} \times \frac{180}{\pi} \] Cancel \(\pi\) from numerator and denominator: \[ \text{degrees} = \frac{13 \times 180}{15} \] Calculate: \[ \text{degrees} = \frac{2340}{15} \] Divide: \[ \text{degrees} = 156 \] The answer is 156 degrees.