Question

1. convert the given angle measure from degrees to radians. - 124°
2. convert the given angle measure from radians to degrees. 3π/8

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180}\). For \(- 124^{\circ}\), we have \(-124\times\frac{\pi}{180}\).

Step2: Simplify the fraction

Simplify \(\frac{-124\pi}{180}\). Divide numerator and denominator by 4: \(\frac{-124\div4}{180\div4}\pi=\frac{-31}{45}\pi\) radians.

Step3: Use the conversion formula for radians to degrees

To convert radians to degrees, use the formula \( \text{Degrees}=\text{Radians}\times\frac{180}{\pi}\). For \(\frac{3\pi}{8}\), we have \(\frac{3\pi}{8}\times\frac{180}{\pi}\).

Step4: Simplify the expression

The \(\pi\) terms cancel out. Then calculate \(\frac{3\times180}{8}=\frac{540}{8} = 67.5^{\circ}\)

Answer:

• For \(-124^{\circ}\), the angle in radians is \(-\frac{31\pi}{45}\) radians.
• For \(\frac{3\pi}{8}\) radians, the angle in degrees is \(67.5^{\circ}\)