Question

how many degrees are equivalent to \\(\frac{3\pi}{4}\\) radians?\
\\(\bigcirc\\) a. \\(68^\circ\\)\
\\(\bigcirc\\) b. \\(75^\circ\\)\
\\(\bigcirc\\) c. \\(135^\circ\\)\
\\(\bigcirc\\) d. \\(270^\circ\\)

Explanation:

Step1: Recall radian to degree conversion formula

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

Step2: Substitute the given radian value

We have \( \frac{3\pi}{4} \) radians. Substitute into the formula: \( \frac{3\pi}{4} \times \frac{180^\circ}{\pi} \)

Step3: Simplify the expression

The \( \pi \) terms cancel out: \( \frac{3}{4} \times 180^\circ = 3 \times 45^\circ = 135^\circ \)

Answer:

C. \( 135^\circ \)