Evaluate exactly.
-$\cos \left( \sin ^ { - 1 } \left( \frac { - 5 } { 13 } \right) \right)$
A) $\frac { 5 } { 13 }$
B) $\frac { - 5 } { 12 }$
C) $\frac { - 12 } { 13 }$
D) $\frac { 12 } { 13 }$

Question

Quizplus · Accepted Answer

The expression $\cos \left( \sin ^ { - 1 } \left( \frac { - 5 } { 13 } \right) \right)$ asks for the cosine of an angle whose sine is $\frac{-5}{13}$. In a right triangle, if the opposite side is -5 and the hypotenuse is 13, the adjacent side (using Pythagoras' theorem) would be $\sqrt{13^2 - (-5)^2} = \sqrt{169 - 25} = \sqrt{144} = 12$. Thus, the cosine, which is the ratio of the adjacent side to the hypotenuse, is $\frac{12}{13}$.

Evaluate Exactly cos⁡(sin⁡−1(−513))\cos \left( \sin ^ { - 1 } \left( \frac { - 5 } { 13 } \right) \right)cos(sin−1(13−5​))

Evaluate Exactly $\cos \left( \sin ^ { - 1 } \left( \frac { - 5 } { 13 } \right) \right)$