MATH SOLVE

2 months ago

Q:
# LAST RADIANS AND ARC LENGTH PLZ HELP

Accepted Solution

A:

We have that the arc and the angle that it subtends are proportional in a circle. In plain words, if the angle is doubled, the arclength is also doubled. We know that 2Ο is the total amount of radians in a circle and it corresponds to the whole circumference. Suppose that x is the fraction of the circumference that 5Ο/6 radians subtend. By proportionality, we have the following equation:

[tex] \frac{1circumf. }{2\pi} = \frac{x}{\frac{5\pi}{6}} [/tex].

Multiplying both sides with 5pi/6 we get:

[tex] \frac{5\pi}{6} * \frac{1}{2\pi} =x[/tex]

Hence, x=5/12

[tex] \frac{1circumf. }{2\pi} = \frac{x}{\frac{5\pi}{6}} [/tex].

Multiplying both sides with 5pi/6 we get:

[tex] \frac{5\pi}{6} * \frac{1}{2\pi} =x[/tex]

Hence, x=5/12