Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To convert [tex]\(50^{\circ}\)[/tex] to radian measure in terms of [tex]\(\pi\)[/tex]:
1. Understand the conversion factor:
To convert degrees to radians, we use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex], because [tex]\(180^{\circ} \equiv \pi\)[/tex] radians.
2. Apply the conversion:
Multiply the degree measure by the conversion factor.
[tex]\[ 50^{\circ} \times \frac{\pi}{180} \][/tex]
3. Perform the multiplication:
[tex]\[ 50 \times \frac{\pi}{180} = \frac{50\pi}{180} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{50\pi}{180} = \frac{5\pi}{18} \][/tex]
Thus, the radian measure of [tex]\(50^{\circ}\)[/tex] in terms of [tex]\(\pi\)[/tex] is [tex]\(\frac{5\pi}{18}\)[/tex].
Now, let's compare this with the given options:
- [tex]\(\frac{5}{27} \pi\)[/tex]
- [tex]\(\frac{5}{9} \pi\)[/tex]
- [tex]\(\frac{5}{18} \pi\)[/tex]
- [tex]\(\frac{5}{36} \pi\)[/tex]
Clearly, [tex]\(\frac{50^\circ}\)[/tex] in radian measure corresponds to the option [tex]\(\frac{5}{18} \pi\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{\frac{5}{18} \pi} \][/tex]
1. Understand the conversion factor:
To convert degrees to radians, we use the conversion factor [tex]\(\frac{\pi}{180}\)[/tex], because [tex]\(180^{\circ} \equiv \pi\)[/tex] radians.
2. Apply the conversion:
Multiply the degree measure by the conversion factor.
[tex]\[ 50^{\circ} \times \frac{\pi}{180} \][/tex]
3. Perform the multiplication:
[tex]\[ 50 \times \frac{\pi}{180} = \frac{50\pi}{180} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{50\pi}{180} = \frac{5\pi}{18} \][/tex]
Thus, the radian measure of [tex]\(50^{\circ}\)[/tex] in terms of [tex]\(\pi\)[/tex] is [tex]\(\frac{5\pi}{18}\)[/tex].
Now, let's compare this with the given options:
- [tex]\(\frac{5}{27} \pi\)[/tex]
- [tex]\(\frac{5}{9} \pi\)[/tex]
- [tex]\(\frac{5}{18} \pi\)[/tex]
- [tex]\(\frac{5}{36} \pi\)[/tex]
Clearly, [tex]\(\frac{50^\circ}\)[/tex] in radian measure corresponds to the option [tex]\(\frac{5}{18} \pi\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{\frac{5}{18} \pi} \][/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.