Find the exact value of the composition.
-$\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$
A) $- \frac { 3 } { 5 }$
B) $\frac { 1 } { 5 }$
C) $- \frac { 4 } { 5 }$
D) $\frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

The expression $\cos(\sin^{-1}(\frac{4}{5}))$ asks for the cosine of an angle whose sine is $\frac{4}{5}$. In a right triangle, if the opposite side over the hypotenuse is $\frac{4}{5}$, then by the Pythagorean theorem, the adjacent side (which corresponds to the cosine of the angle) must be $\frac{3}{5}$, assuming a positive value in the principal range of $\sin^{-1}$.

Find the Exact Value of the Composition cos⁡(sin⁡−145)\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)cos(sin−154​)

Find the Exact Value of the Composition $\cos \left( \sin ^ { - 1 } \frac { 4 } { 5 } \right)$