Posted by John on .
Find an angle between 0 and 2ð that is coterminal with the given angle.
A sector of a circle has a central angle of 60°. Find the area of the sector if the radius of the circle is 3 mi.
-8pi/3 is coterminal with -8pi/3 ± 6pi/3
So, these are: -8pi/3 -2pi/3, 4pi/3 ... and we have a winner!
60° is 1/6 of 360°. So, the are is 1/6 of a whole circle, or 1/6 * pi * 3^2 = 3/2 pi
add 2π to -8π/3
to get -2π/3
add another 2π to get
check by taking sin, cos and tan of both -8π/3 and 4π/3.
you should get the same result for each trig function.
(in degrees we started with -480
added 720° to get 240° which lies between 0 and 360)