Question

convert each degree measure into radians. reduce if possible. 13) 315° 14) 285° 15) 240° 16) 160°

Explanation:

Step1: Recall the conversion formula

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

Step2: Convert \(315^{\circ}\) to radians

For \(315^{\circ}\), \(315\times\frac{\pi}{180}=\frac{315\pi}{180}=\frac{7\pi}{4}\)

Step3: Convert \(285^{\circ}\) to radians

For \(285^{\circ}\), \(285\times\frac{\pi}{180}=\frac{285\pi}{180}=\frac{19\pi}{12}\)

Step4: Convert \(240^{\circ}\) to radians

For \(240^{\circ}\), \(240\times\frac{\pi}{180}=\frac{240\pi}{180}=\frac{4\pi}{3}\)

Step5: Convert \(160^{\circ}\) to radians

For \(160^{\circ}\), \(160\times\frac{\pi}{180}=\frac{160\pi}{180}=\frac{8\pi}{9}\)

Answer:

1. \(\frac{7\pi}{4}\) radians
2. \(\frac{19\pi}{12}\) radians
3. \(\frac{4\pi}{3}\) radians
4. \(\frac{8\pi}{9}\) radians