Question

what is 4 radians converted to degrees? if necessary, round your answer to the nearest degree.
○ 13°
○ 45°
○ 229°
○ 720°

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 value of radians

We are given 4 radians. Substitute \( \text{Radians} = 4 \) into the formula:
\( \text{Degrees} = 4 \times \frac{180^\circ}{\pi} \)

Step3: Calculate the value

First, calculate \( 4\times180 = 720 \), then divide by \( \pi \):
\( \text{Degrees} = \frac{720^\circ}{\pi} \approx \frac{720}{3.1416} \approx 229.18^\circ \)

Step4: Round to the nearest degree

Rounding \( 229.18^\circ \) to the nearest degree gives \( 229^\circ \)

Answer:

229° (corresponding to the option "229°")