Find the exact value of the expression, if possible. Do not use a calculator.
-$\cos \left( \sin ^ { - 1 } x \right)$
A) $\sqrt { 1 - x ^ { 2 } }$
B) $\sqrt { x ^ { 2 } + 1 }$
C) $\sqrt { \mathrm { x } ^ { 2 } - 1 }$
D) $\frac { \sqrt { x ^ { 2 } + 1 } } { x }$

Question

Quizplus · Accepted Answer

The expression $\cos(\sin^{-1}x)$ can be understood through a right triangle, where if $\sin^{-1}x$ is an angle, then the opposite side over the hypotenuse is $x/1$. Using the Pythagorean theorem, the adjacent side (which corresponds to the cosine of the angle) is $\sqrt{1 - x^2}$.

Find the Exact Value of the Expression, If Possible cos⁡(sin⁡−1x)\cos \left( \sin ^ { - 1 } x \right)cos(sin−1x)

Find the Exact Value of the Expression, If Possible $\cos \left( \sin ^ { - 1 } x \right)$