Write the trigonometric expression as an algebraic expression in u.
-$\cos \left( \sin ^ { - 1 } \mathrm { u } \right)$
A) $\sqrt { u ^ { 2 } + 1 }$
B) $\sqrt { 1 - \mathrm { u } ^ { 2 } }$
C) $\sqrt { \mathrm { u } ^ { 2 } - 1 }$
D) $\frac { \sqrt { \mathrm { u } ^ { 2 } + 1 } } { \mathrm { u } }$

Question

Quizplus · Accepted Answer

The expression $\cos(\sin^{-1}(u))$ can be understood through a right triangle, where if $\sin^{-1}(u)$ represents an angle, then $u$ is the opposite side over the hypotenuse. To find the cosine of that angle, we need the adjacent side over the hypotenuse. Using the Pythagorean theorem, the adjacent side is $\sqrt{1-u^2}$, making the expression $\cos(\sin^{-1}(u)) = \sqrt{1-u^2}$.

Write the Trigonometric Expression as an Algebraic Expression in U cos⁡(sin⁡−1u)\cos \left( \sin ^ { - 1 } \mathrm { u } \right)cos(sin−1u)

Write the Trigonometric Expression as an Algebraic Expression in U $\cos \left( \sin ^ { - 1 } \mathrm { u } \right)$