Let θ be an angle in quadrant IV such that sinθ=-3/4. Find the exact values of secθ and cotθ.

cos2(θ) + sin2(θ) = 1

sec(θ) = 1/cos(θ)

cot(θ) = cos(x)/sin(θ)

sin(θ) = -3/4

cos2(θ) + sin2(θ) = 1

cos2(θ) = 1 - sin2(θ)

cos2(θ) = 1 - 9/16 = 7/16

cos(θ) = ±√(7/16) = √7/16  (cosine is positive in Q IV)

sec(θ) = 1/cos(θ) = 4/√7

cot(θ) = cos(θ)/sin(θ) = (4/√7)/(-3/4) = -16√7/21

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