Question

convert the angle -3 radians to degrees, rounding to the nearest 10th.

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 value

We are given \( -3 \) radians. Substitute \( \text{Radians} = -3 \) into the formula:
\( \text{Degrees} = -3 \times \frac{180^\circ}{\pi} \)

Step3: Calculate the value

First, calculate \( \frac{180}{\pi} \approx 57.2958 \) (approximate value). Then multiply by \( -3 \):
\( -3 \times 57.2958 \approx -171.8874 \)

Step4: Round to the nearest tenth

Rounding \( -171.8874 \) to the nearest tenth gives \( -171.9 \)

Answer:

\( -171.9^\circ \)