Question 1077636: Hi can someone help me with this problem please? THANK YOU!
State the exact value of t,given cot t=-1/root3 and t[0,2pi)terminates QII
Select one
a. 5pi/6
b.7pi/6
c.pi/3
d.2pi/3
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cot(t) = -1/sqrt(3)
since cot(t) = 1/tan(t), then:
1/tan(t) = -1/sqrt(3)
solve for tan(t) to get tan(t) = -sqrt(3)
if you assume tan(t) is positive, you will get the equivalent angle in the first quadrant.
use your calculator to solve for tan^-1(sqrt(3)) and you will find that t = 60 degrees.
that's in the first quadrant.
you want the equivalent angle in the second quadrant.
the angle in the second quadrant is equal to 180 minus the angle in the first quadrant.
that makes the angle equal to 180 - 60 = 120 degrees.
the equivalent angle in radians is equal to 120 * pi / 180 = 2/3 * pi.
that's selection d.
if your calculator is set to radians, then your answer will be as follows:
tan^-1(sqrt(3)) = 1.047197551 radians
divide that by pi to get tan^-1(sqrt(3)) = .333333333 * pi radians.
since .3333333 is equal to 1/3, then the calculator is telling you that tan^-1(sqrt(3)) is equal to 1/3 * pi radians.
that's in the first quadrant.
the equivalent angle in the second quadrant is equal to pi - 1/3 * pi which is equal to 1/3 * pi.
that's selection d again.
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