Let θ be an angle in quadrant IV such that sinθ = -2/5 . Find the exact values of secθ and tanθ.

1 answer:

8 0

If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,

sin²(θ) + cos²(θ) = 1 ==> cos(θ) = +√(1 - sin²(θ)) = √21/5

Then

sec(θ) = 1/cos(θ) = 5/√21

and

tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21

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