Find the exact value of the expression, if possible. Do not use a calculator.
-$\cos \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$
A) $\frac { 4 } { 5 }$
B) $\frac { 1 } { 5 }$
C) $- \frac { 3 } { 5 }$
D) $- \frac { 4 } { 5 }$

Question

Quizplus · Accepted Answer

The expression $\cos(\sin^{-1}(\frac{3}{5}))$ asks for the cosine of an angle whose sine is $\frac{3}{5}$. In a right triangle, if the opposite side is 3 and the hypotenuse is 5, the adjacent side (using the Pythagorean theorem) would be $\sqrt{5^2 - 3^2} = \sqrt{25 - 9} = \sqrt{16} = 4$. Thus, the cosine of this angle, which is the ratio of the adjacent side to the hypotenuse, is $\frac{4}{5}$.

Find the Exact Value of the Expression, If Possible cos⁡(sin⁡−135)\cos \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)cos(sin−153​)

Find the Exact Value of the Expression, If Possible $\cos \left( \sin ^ { - 1 } \frac { 3 } { 5 } \right)$