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Math  /  Trigonometry

Question5. [-/3 Points] DETAILS MY NOTES COHENPCALC7 7.1.010.
Convert the radian measures to degrees. (a) 2π2 \pi □\square (b) 3π/23 \pi / 2 □\square (c) 3π3 \pi □\square Need Help? Read It Submit Answer
6. [-/3 Points]
DETAILS MY NOTES COHENPCALC7 7.1.012. Convert the radian measures to degrees. (a) 3π/63 \pi / 6 □\square (b) 7π/67 \pi / 6 □\square (c) 0 □\square。 Need Help? Read It Watch It Submit Answer

Studdy Solution

STEP 1

1. The conversion factor between radians and degrees is 180∘/π180^\circ/\pi.
2. To convert a radian measure to degrees, multiply the radian measure by the conversion factor.

STEP 2

1. Convert each radian measure to degrees for Problem 5.
2. Convert each radian measure to degrees for Problem 6.

STEP 3

Convert 2π2\pi radians to degrees.
2π×180∘π=360∘ 2\pi \times \frac{180^\circ}{\pi} = 360^\circ

STEP 4

Convert 3π2\frac{3\pi}{2} radians to degrees.
3π2×180∘π=270∘ \frac{3\pi}{2} \times \frac{180^\circ}{\pi} = 270^\circ

STEP 5

Convert 3π3\pi radians to degrees.
3π×180∘π=540∘ 3\pi \times \frac{180^\circ}{\pi} = 540^\circ

STEP 6

Convert 3π6\frac{3\pi}{6} radians to degrees.
3π6×180∘π=90∘ \frac{3\pi}{6} \times \frac{180^\circ}{\pi} = 90^\circ

STEP 7

Convert 7π6\frac{7\pi}{6} radians to degrees.
7π6×180∘π=210∘ \frac{7\pi}{6} \times \frac{180^\circ}{\pi} = 210^\circ

STEP 8

Convert 00 radians to degrees.
0×180∘π=0∘ 0 \times \frac{180^\circ}{\pi} = 0^\circ
The solutions are: (a) 2π2\pi radians = 360∘360^\circ (b) 3π2\frac{3\pi}{2} radians = 270∘270^\circ (c) 3π3\pi radians = 540∘540^\circ
(a) 3π6\frac{3\pi}{6} radians = 90∘90^\circ (b) 7π6\frac{7\pi}{6} radians = 210∘210^\circ (c) 00 radians = 0∘0^\circ

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