Use the trigonometric substitution to select the algebraic expression as a trigonometric function of$\text { } \theta \text {, where } 0

Question

Use the trigonometric substitution to select the algebraic expression as a trigonometric function of$\text {  } \theta \text {, where } 0 < \theta < \frac { \pi } { 2 } \text {. }$ $\sqrt { 25 x ^ { 2 } + 36 } , 5 x = 6 \tan \theta$ 
A) $5 \tan \theta$
B) $25 \sec \theta$
C) $25 \tan \theta$
D) $- 5 \sec \theta$
E) $6 \sec \theta$

Quizplus · Accepted Answer

Using the substitution $5x = 6 \tan \theta$, we have $x = \frac{6}{5} \tan \theta$. Then, $\sqrt{25x^2 + 36} = \sqrt{36 \tan^2 \theta + 36} = \sqrt{36(\tan^2 \theta + 1)} = \sqrt{36 \sec^2 \theta} = 6 \sec \theta$.

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