Answer:
[tex]\frac{12}{13}[/tex]
Step-by-step explanation:
We are asked to find the exact value of [tex]\cos(\arcsin \frac{5}{13})[/tex].
Firstly, let's call [tex]y = \arcsin \frac{5}{13}[/tex] ⇒ [tex]\sin y=\frac{5}{13}[/tex].
Since [tex]\cos(\arcsin \frac{5}{13})=\cos y[/tex]
[tex]\cos(\arcsin \frac{5}{13}) = \sqrt{1-\sin^2y}=\sqrt{1-(\frac{5}{13})^2}=\sqrt{1-\frac{25}{169}}=\sqrt{\frac{144}{169}}=\frac{12}{13}[/tex]
