Question

convert 1 radian to degrees. round your answer to the nearest degree.
convert \frac{3\pi}{8} radians to degrees.

Explanation:

First Sub - Question: Convert 1 radian to degrees. Round your answer to the nearest degree.

Step1: Recall the conversion formula

The formula to convert radians to degrees is \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi} \).

Step2: Substitute the value of radians

We have 1 radian. Substituting into the formula, we get \( 1\times\frac{180^{\circ}}{\pi} \).

Step3: Calculate the value

\( \frac{180^{\circ}}{\pi}\approx\frac{180}{3.1416}\approx57.3^{\circ}\approx57^{\circ} \) (rounded to the nearest degree).

Step1: Recall the conversion formula

The formula to convert radians to degrees is \( \text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi} \).

Step2: Substitute the value of radians

We have \( \frac{3\pi}{8} \) radians. Substituting into the formula, we get \( \frac{3\pi}{8}\times\frac{180^{\circ}}{\pi} \).

Step3: Simplify the expression

The \( \pi \) terms cancel out, and we have \( \frac{3\times180^{\circ}}{8}=\frac{540^{\circ}}{8} = 67.5^{\circ}\).

Answer:

\( 57 \)

Second Sub - Question: Convert \( \frac{3\pi}{8} \) radians to degrees.