Given Tangent Theta= -4/5, Theta in quadrant 2 , how do you find Cos Theta?

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Answer 1 · 2016-07-12T18:50:11

#costheta=-5/sqrt41#.

Given that #tantheta=-4/5, theta in Q_(II)#

Recall that #costheta=1/sectheta# and, #tan# and #sec# are related

by the Identity #: sec^2theta=1+tan^2theta.#

#:. sec^2theta=1+(-4/5)^2=1+16/25=41/25.#

#:. sectheta=+-sqrt41/5 rArr costheta=+-5/sqrt41#

But, #theta in Q_(II) rArr costheta# is #-ve#.

Hence, #costheta=-5/sqrt41#.