Question

match each angle measure in degrees in the left column with its corresponding measure in radians in the right column.

1. 60° a. \\( \frac{\pi}{8} \\)

ii. -15° b. \\( -\frac{\pi}{12} \\)
iii. -200° c. \\( \frac{4\pi}{3} \\)
iv. -108° d. \\( -\frac{10\pi}{9} \\)
v. 22.5° e. \\( -\frac{3\pi}{5} \\)
vi. 240° f. \\( \frac{\pi}{3} \\)

Explanation:

Step1: Use the conversion formula

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

Step2: Convert \(60^{\circ}\)

For \(60^{\circ}\), \(60\times\frac{\pi}{180}=\frac{\pi}{3}\) (matches option F)

Step3: Convert \(- 15^{\circ}\)

For \(-15^{\circ}\), \(-15\times\frac{\pi}{180}=-\frac{\pi}{12}\) (matches option B)

Step4: Convert \(-200^{\circ}\)

For \(-200^{\circ}\), \(-200\times\frac{\pi}{180}=-\frac{10\pi}{9}\) (matches option D)

Step5: Convert \(-108^{\circ}\)

For \(-108^{\circ}\), \(-108\times\frac{\pi}{180}=-\frac{3\pi}{5}\) (matches option E)

Step6: Convert \(22.5^{\circ}\)

For \(22.5^{\circ}\), \(22.5\times\frac{\pi}{180}=\frac{\pi}{8}\) (matches option A)

Step7: Convert \(240^{\circ}\)

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

Answer:

I. F. \(\frac{\pi}{3}\)
II. B. \(-\frac{\pi}{12}\)
III. D. \(-\frac{10\pi}{9}\)
IV. E. \(-\frac{3\pi}{5}\)
V. A. \(\frac{\pi}{8}\)
VI. C. \(\frac{4\pi}{3}\)