To convert degrees to radians, you use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex]. Here's the step-by-step process for converting [tex]\(-36^\circ\)[/tex] to radians:
1. Write down the given angle in degrees:
[tex]\[
\theta = -36^\circ
\][/tex]
2. Use the conversion factor:
Radians = Degrees [tex]\(*\)[/tex] [tex]\(\frac{\pi}{180}\)[/tex]
3. Substitute the given degrees into the conversion factor:
[tex]\[
\theta_{\text{radians}} = -36 \times \frac{\pi}{180}
\][/tex]
4. Simplify the fraction:
[tex]\[
\theta_{\text{radians}} = -36 \times \frac{\pi}{180} = -\frac{36\pi}{180}
\][/tex]
5. Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 36:
[tex]\[
\theta_{\text{radians}} = -\frac{36\pi}{180} = -\frac{\pi}{5}
\][/tex]
Therefore, [tex]\(-36^\circ\)[/tex] converted to radians is:
[tex]\[
-\frac{\pi}{5}
\][/tex]
Given the multiple choice options:
- [tex]\(-5 \pi\)[/tex]
- [tex]\(-\frac{5}{\pi}\)[/tex]
- [tex]\(-\frac{\pi}{5}\)[/tex]
- [tex]\(-\frac{1}{5}\)[/tex]
The correct answer is:
[tex]\[
-\frac{\pi}{5}
\][/tex]
