Find an algebraic expression that is equivalent to the expression.. $\cos ( \arcsin 4 x )$
A) $\frac { \sqrt { 1 + 16 x ^ { 2 } } } { 1 + 16 x ^ { 2 } }$
B) $\frac { \sqrt { 1 - 16 x ^ { 2 } } } { 1 - 16 x ^ { 2 } }$
C) $\sqrt { 16 x ^ { 2 } - 1 }$
D) $\sqrt { 1 + 16 x ^ { 2 } }$
E) $\sqrt { 1 - 16 x ^ { 2 } }$

Question

Find an algebraic expression that is equivalent to the expression..​ $\cos ( \arcsin 4 x )$ ​
A) $\frac { \sqrt { 1 + 16 x ^ { 2 } } } { 1 + 16 x ^ { 2 } }$
B) $\frac { \sqrt { 1 - 16 x ^ { 2 } } } { 1 - 16 x ^ { 2 } }$
C) $\sqrt { 16 x ^ { 2 } - 1 }$
D) $\sqrt { 1 + 16 x ^ { 2 } }$
E) $\sqrt { 1 - 16 x ^ { 2 } }$

Quizplus · Accepted Answer

The expression $\cos ( \arcsin 4x )$ can be simplified using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$. If $\sin \theta = 4x$, then $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - (4x)^2} = \sqrt{1 - 16x^2}$.

Find an Algebraic Expression That Is Equivalent to the Expression cos⁡(arcsin⁡4x)\cos ( \arcsin 4 x )cos(arcsin4x)

Find an Algebraic Expression That Is Equivalent to the Expression $\cos ( \arcsin 4 x )$