If #cot theta = -9/2# with #theta# in quadrant 2, find #sin theta? #

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Answer 1 · 2018-02-17T16:30:12

#sin theta = 0.976#

The negative sign indicates that it is an angle in the second quadrant - an obtuse angle. Link it to an acute angle.

Using a calculator:

#cot theta = -2/9 hArr tan theta = -9/2 = -4.5#
#tan^-1(9/2) = 77.5°#

The obtuse angle is #180-77.5 = 102.5°#

#sin 167.5° = 0.976#

Using a right- angled triangle.

#cot theta = a/o = -2/9#

Find the length of the hypotenuse using Pythagoras' Theorem.

#h^2 = 2^2 +9^2 = 85#

#h = sqrt85#

In the second quadrant #sin theta# is positive.

#sin theta = o/h = 9/sqrt85 = 0.976#