Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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]
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]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.