Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![### Converting Between Degrees and Radians: Examples
#### Convert \( \frac{13\pi}{6} \) to degrees:
**Solution:**
\[ \frac{13\pi}{6} \quad \text{radians} \]
First, we use the conversion factor that \( \pi \) radians is equivalent to \( 180^\circ \):
\[ \frac{13\pi}{6} \times \frac{180^\circ}{\pi} = \frac{13 \times 180^\circ}{6} \]
\[ \frac{13 \times 180^\circ}{6} = 13 \times 30^\circ = 390^\circ \]
So, \( \frac{13\pi}{6} \) radians is equal to \( 390^\circ \).
#### Convert \( 896^\circ \) to radians:
**Solution:**
\[ 896^\circ \]
To convert degrees to radians, we use the conversion factor that \( 180^\circ \) is equivalent to \( \pi \) radians:
\[ 896^\circ \times \frac{\pi \, \text{radians}}{180^\circ} = \frac{896\pi}{180} \]
This can be simplified further by dividing both numerator and denominator by their greatest common divisor:
\[ \frac{896\pi}{180} = \frac{448\pi}{90} = \frac{224\pi}{45} \]
Thus, \( 896^\circ \) converted to radians is:
\[ \frac{224\pi}{45} \, \text{radians} \]
These conversions demonstrate the process of switching between degrees and radians, which is fundamental in trigonometry and various applications in mathematics and physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a49397d-2847-420e-bdfe-93d5dc178c48%2F2643d73d-59f9-4fab-aca9-535f1eea785c%2Febkrbm4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Converting Between Degrees and Radians: Examples
#### Convert \( \frac{13\pi}{6} \) to degrees:
**Solution:**
\[ \frac{13\pi}{6} \quad \text{radians} \]
First, we use the conversion factor that \( \pi \) radians is equivalent to \( 180^\circ \):
\[ \frac{13\pi}{6} \times \frac{180^\circ}{\pi} = \frac{13 \times 180^\circ}{6} \]
\[ \frac{13 \times 180^\circ}{6} = 13 \times 30^\circ = 390^\circ \]
So, \( \frac{13\pi}{6} \) radians is equal to \( 390^\circ \).
#### Convert \( 896^\circ \) to radians:
**Solution:**
\[ 896^\circ \]
To convert degrees to radians, we use the conversion factor that \( 180^\circ \) is equivalent to \( \pi \) radians:
\[ 896^\circ \times \frac{\pi \, \text{radians}}{180^\circ} = \frac{896\pi}{180} \]
This can be simplified further by dividing both numerator and denominator by their greatest common divisor:
\[ \frac{896\pi}{180} = \frac{448\pi}{90} = \frac{224\pi}{45} \]
Thus, \( 896^\circ \) converted to radians is:
\[ \frac{224\pi}{45} \, \text{radians} \]
These conversions demonstrate the process of switching between degrees and radians, which is fundamental in trigonometry and various applications in mathematics and physics.
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