Question

matching 1 point
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 } \\)
i.
ii.
iii.
iv.
v.
vi.

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 \(60^{\circ}\), \(60\times\frac{\pi}{180}=\frac{\pi}{3}\)

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

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

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

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

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

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

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

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

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

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

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. \(\frac{4\pi}{3}\)