find the value of cosine function

tan θ = -2/3 and angle θ lies in the second quadrant, what is the value of cos θ

Expert Answers

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tan x = -2/3

We need to find cosx such that x is in the second quadrant.

We know that:

sinx/cosx = tanx = -2/3

==> sinx = (-2/3) cosx

Also,

sin^2 x + cos^2 x= 1

==> (-2/3)cosx)^2 + cos^2 x = 1

==> (4/9)cos^2 x + cos^2 x = 1

==> (13/9)cos^2 x = 1

==> cos^2 x= 9/13

==> cosx = +-3/sqrt13= 3sqrt13/13

Since x is in the second quadrant, then cosx is negative.

==> cosx = -3sqrt13/13

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