Complete the identity.
-$\cos \left( \sin ^ { - 1 } v \right) = ?$
A) $\sqrt { v ^ { 2 } + 1 }$
B) $\sqrt { 1 - \mathrm { v } ^ { 2 } }$
C) $\frac { \sqrt { v ^ { 2 } + 1 } } { v }$
D) $\sqrt { v ^ { 2 } - 1 }$

Question

Quizplus · Accepted Answer

The identity can be derived using the Pythagorean theorem applied to a right triangle, where if $v = \sin(\theta)$, then $\cos(\theta) = \sqrt{1 - v^2}$. This is because $\sin^2(\theta) + \cos^2(\theta) = 1$, leading to $\cos(\theta) = \sqrt{1 - \sin^2(\theta)} = \sqrt{1 - v^2}$.

Complete the Identity cos⁡(sin⁡−1v)=?\cos \left( \sin ^ { - 1 } v \right) = ?cos(sin−1v)=?

Complete the Identity $\cos \left( \sin ^ { - 1 } v \right) = ?$