Let's consider what the problem wants us to find:
- fractional part covered by the labeled angle
Let's find the fractional part:
⇒ the fractional part is equal:
[tex]\frac{degree-covered-by-angle}{total-angle} =\frac{100}{180} =\frac{2*2*5*5}{2*2*3*3*5} =\frac{5}{3*3} =\frac{5}{9}[/tex]
Answer: The angle 100 degrees covers 5/9 of a semicircle.
Let's find the angle measure in radians:
⇒ we know that [tex]2\pi[/tex] radians are equal to 360 degrees
⇒ to convert any degree to radians, you must multiply [tex]\frac{\pi }{180}[/tex]
so [tex]100*\frac{\pi }{180} =\frac{100\pi }{180} =\frac{10}{18} \pi =\frac{5}{9} \pi[/tex]
Answer: The angle 100 degrees in radians is [tex]\frac{5}{9} \pi[/tex] which in terms of [tex]\pi[/tex] is
5/9
Hope that helps!
