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

question 46

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }$ .Then find sin θ and cos θ.​ $4 = \sqrt { 64 - x ^ { 2 } } , x = 8 \sin \theta$

• A)​ \(64 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• B)​ \(64 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• C)​ \(8 \sin \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• D)​ \(8 \cos \theta = 4 ; \sin \theta = \pm \frac { \sqrt { 3 } } { 2 } ; \cos \theta = \frac { 1 } { 2 }\)
• E)​ \(8 \cos \theta = 4 ; \sin \theta = \frac { 1 } { 2 } ; \cos \theta = \pm \frac { \sqrt { 3 } } { 2 }\)

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