Question

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

Explanation:

Step1: Use radian-degree conversion formula

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

Step2: Convert 1 radian to degrees

$1 \times \frac{180^\circ}{\pi} \approx 57.2958^\circ$, round to nearest degree: $57^\circ$

Step3: Convert $\frac{3\pi}{8}$ radians to degrees

$\frac{3\pi}{8} \times \frac{180^\circ}{\pi} = \frac{3 \times 180^\circ}{8} = 67.5^\circ$

Answer:

1 radian ≈ $57^\circ$
$\frac{3\pi}{8}$ radians = $67.5^\circ$