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

Multiple Choice

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ,where $- \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$ .Then find sin θ and cos θ. $4 = \sqrt { 16 - x ^ { 2 } } , x = 4 \sin \theta$

A) $16 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1$
B) ​ $4 \cos \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1$
C) ​ $16 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1$
D) ​ $4 \cos \theta = 4 ; \sin \theta = 1 ; \cos \theta = 0$
E) ​ $4 \sin \theta = 4 ; \sin \theta = 0 ; \cos \theta = 1$