Question

convert the angle \\(\frac{7\pi}{12}\\) radians to degrees.

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, we use the formula: \( \text{Degrees} = \text{Radians} \times \frac{180^\circ}{\pi} \)

Step2: Substitute the given radian measure

We have the radian measure \( \frac{7\pi}{12} \). Substitute this into the formula:
\( \frac{7\pi}{12} \times \frac{180^\circ}{\pi} \)
The \( \pi \) terms cancel out:
\( \frac{7}{12} \times 180^\circ \)

Step3: Perform the multiplication

Calculate \( \frac{7 \times 180^\circ}{12} \). First, simplify \( \frac{180}{12} = 15 \). Then, \( 7 \times 15^\circ = 105^\circ \)

Answer:

\( 105^\circ \)