How many degrees are equivalent to $\frac{7}{10}$ radians?

• A. $90$ degrees
• B. $126$ degrees
• C. $252$ degrees
• D. $63$ degrees

Answer: (B)

Verified step by step guidance

1. Recall the conversion formula between radians and degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
2. Identify the given radian measure, which is \(\dfrac{7}{10}\) radians.
3. Substitute the given radian value into the conversion formula: \(\text{degrees} = \dfrac{7}{10} \times \dfrac{180}{\pi}\).
4. Simplify the multiplication by calculating \(\dfrac{7 \times 180}{10 \times \pi}\), which is \(\dfrac{1260}{10\pi}\) degrees.
5. To find the numerical degree value, approximate \(\pi\) as 3.1416 and perform the division, but since the problem asks for the process, stop here before calculating the final number.