Let θ be an angle in quadrant IV such that sinθ = -2/5 .
Find the exact values of secθ and tanθ.
1 answer:
If <em>θ</em> lies in the fourth quadrant, then sin(<em>θ</em>) < 0 and cos(<em>θ</em>) > 0. So we have from the Pythagorean identity,
sin²(<em>θ</em>) + cos²(<em>θ</em>) = 1 ==> cos(<em>θ</em>) = +√(1 - sin²(<em>θ</em>)) = √21/5
Then
sec(<em>θ</em>) = 1/cos(<em>θ</em>) = 5/√21
and
tan(<em>θ</em>) = sin(<em>θ</em>)/cos(<em>θ</em>) = (-2/5)/(√21/5) = -2/√21
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