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In an integral involving √ $(9 - x^{2})$ a student substitutes $x = 3$ sinθ with θ acute. The radical then becomes:

Competition practiceTrigonometry

A3 sinθ
B3 cosθ
C9 cosθ
D3 tanθ

Step-by-Step Solution

√

(9 - x^{2})

= √(9 − 9si

n^{2}

θ) = √(9co

s^{2}

θ) = 3cosθ for acute θ. Forgetting to take the square root of 9 leaves the trap 9cosθ.

Answer: B) 3 cosθ

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