Mills Willis
03/29/2023 · High School
Convert to radian measure. Express your answers be (a) \( 50^{\circ} \) (b) \( 100^{\circ} \) (c) \( 150^{\circ} \)
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Tutor-Verified Answer
Step-by-step Solution
To convert degrees to radians, you can use the conversion factor \(\frac{\pi \text{ radians}}{180^{\circ}}\). The formula to convert degrees to radians is:
\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\]
Now, let's convert each of the given angles:
(a) For \( 50^{\circ} \):
\[
50^{\circ} \times \frac{\pi}{180} = \frac{50\pi}{180} = \frac{5\pi}{18} \text{ radians}
\]
(b) For \( 100^{\circ} \):
\[
100^{\circ} \times \frac{\pi}{180} = \frac{100\pi}{180} = \frac{10\pi}{18} = \frac{5\pi}{9} \text{ radians}
\]
(c) For \( 150^{\circ} \):
\[
150^{\circ} \times \frac{\pi}{180} = \frac{150\pi}{180} = \frac{15\pi}{18} = \frac{5\pi}{6} \text{ radians}
\]
In summary, the conversions are:
- (a) \( 50^{\circ} = \frac{5\pi}{18} \) radians
- (b) \( 100^{\circ} = \frac{5\pi}{9} \) radians
- (c) \( 150^{\circ} = \frac{5\pi}{6} \) radians
Quick Answer
(a) \( 50^{\circ} = \frac{5\pi}{18} \) radians
(b) \( 100^{\circ} = \frac{5\pi}{9} \) radians
(c) \( 150^{\circ} = \frac{5\pi}{6} \) radians
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