Question

find the radian measure for each of the following angles. enter each answer as a reduced fraction involving π.
70° = radians
160° = radians
140° = radians
90° = radians

Explanation:

Step1: Use the conversion formula

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

Step2: Calculate for \(70^{\circ}\)

Substitute \(70\) into the formula: \( \frac{\pi}{180}\times70=\frac{7\pi}{18}\).

Step3: Calculate for \(160^{\circ}\)

Substitute \(160\) into the formula: \( \frac{\pi}{180}\times160=\frac{8\pi}{9}\).

Step4: Calculate for \(140^{\circ}\)

Substitute \(140\) into the formula: \( \frac{\pi}{180}\times140=\frac{7\pi}{9}\).

Step5: Calculate for \(90^{\circ}\)

Substitute \(90\) into the formula: \( \frac{\pi}{180}\times90=\frac{\pi}{2}\).

Answer:

\(70^{\circ}=\frac{7\pi}{18}\) radians, \(160^{\circ}=\frac{8\pi}{9}\) radians, \(140^{\circ}=\frac{7\pi}{9}\) radians, \(90^{\circ}=\frac{\pi}{2}\) radians.