Given that sin t=(-2/3) and that P(t) is a point in the third quadrant, what is cos (t)?

1 Answer
Apr 5, 2018

#cos t = sqrt5/3#

Explanation:

#sin^2 t + cos^2 t = 1#

Given that #sin t = -2/3#
#sin^2t = (-2/3)^2=4/9#

Therefore #cos^2t = 1-4/9 = 5/9#

#cos t = ± {sqrt5}/3#

Since cos is negative in the third quadrant we can rule out the positive solution.

Therefore #cos t = sqrt5/3#