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

question 72

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of $\theta$ , where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .Then find sin $\theta$ and cos $\theta$ .
$3 \sqrt { 3 } = \sqrt { 81 - 9 x ^ { 2 } } , x = 3 \cos \theta$

• A) \(\sin \theta = 3 ; \sin \theta = \frac { \sqrt { 3 } } { 3 } ; \cos \theta = \frac { \sqrt { 6 } } { 3 }\)
• B) \(3 \sin \theta = 3 ; \sin \theta = 0 ; \cos \theta = 1\)
• C) \(\sin \theta = \sqrt { 3 } ; \sin \theta = \frac { \sqrt { 3 } } { 3 } ; \cos \theta = \frac { \sqrt { 6 } } { 3 }\)
• D) \(9 \sin \theta = 3 \sqrt { 3 } ; \sin \theta = \frac { \sqrt { 3 } } { 3 } ; \cos \theta = \frac { \sqrt { 6 } } { 3 }\)
• E) \(3 \cos \theta = 3 ; \sin \theta = 1 ; \cos \theta = 0\)

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