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If 2sinθ + 3cosθ = 2, then 3sinθ − 2cosθ equals:

Competition practiceTrigonometry

A±2
B±√5
C±3
D±13

Step-by-Step Solution

(2 s in θ + 3 cos θ)^{2} + (3 s in θ - 2 cos θ)^{2} = 13 (s i

n^{2}

θ +

co

s^{2}

θ) = 13, since the cross terms cancel. So

(3 s in θ - 2 cos θ)^{2} = 13 - 4 = 9

, giving ±3.

Answer: C) ±3

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