Change [tex]$50^{\circ}$[/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 an angle from degrees to radians, you use the conversion factor [tex]\( \frac{\pi}{180} \)[/tex]. This means you multiply the degree measure by [tex]\( \frac{\pi}{180} \)[/tex].

Given the angle [tex]\( 50^\circ \)[/tex]:

1. Start by writing down the conversion formula:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]

2. Substitute [tex]\( 50 \)[/tex] for the degree measure:
[tex]\[ \text{radians} = 50 \times \frac{\pi}{180} \][/tex]

3. Simplify the fraction:
[tex]\[ \text{radians} = \frac{50 \pi}{180} \][/tex]

4. Simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 10:
[tex]\[ \frac{50 \pi}{180} = \frac{5 \pi}{18} \][/tex]

So, [tex]\( 50^\circ \)[/tex] is equal to [tex]\( \frac{5}{18} \pi \)[/tex] radians.

Hence, the correct answer is:
[tex]\[ \boxed{\frac{5}{18} \pi} \][/tex]