Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .
A)4 sin θ
B)- 4 cos θ
C)4 cos θ
D)16 sin θ
E)16 cos θ

Question

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where  .  ​
A)4 sin θ 
B)- 4 cos θ 
C)4 cos θ 
D)16 sin θ 
E)16 cos θ

Quizplus · Accepted Answer

We can use the trigonometric substitution x = 2tanθ to simplify the expression. 
Then, we have: 
$\sqrt{4x^2+11} = \sqrt{4(2	an	heta)^2+11}=\sqrt{16	an^2	heta+11}= \sqrt{11}\sqrt{\frac{16	an^2	heta}{11}+1} = \sqrt{11}\sec	heta.$ 
Thus, the expression becomes: 
$4x\sqrt{4x^2+11} = 8	an	heta\cdot \sqrt{11}\sec	heta = 8\sqrt{11} \sin	heta.$ 
Therefore, the answer is (C) 4cosθ.

Use the Trigonometric Substitution to Rewrite the Algebraic Expression as a Trigonometric