Question 10 (5 points)

Change [tex][tex]$50^{\circ}$[/tex][/tex] to radian measure in terms of [tex]$\pi$[/tex].

A. [tex]\frac{5}{27} \pi[/tex]
B. [tex]\frac{5}{9} \pi[/tex]
C. [tex]\frac{5}{18} \pi[/tex]
D. [tex]\frac{5}{36} \pi[/tex]



Answer :

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]