Question

Find the exact value of cos (arcsin (five divided by thirteen)). thirteen over twelve three times the square root of thirteen divided by thirteen twelve over thirteen two times the square root of thirteen divided by thirteen

Answer 1

`(12)/(13)`

Explanation:

We are asked to find the exact value of
`\cos(\arcsin (5)/(13))`.

Firstly, let's call
`y = \arcsin (5)/(13)` ⇒
`\sin y=(5)/(13)`.

Since
`\cos(\arcsin (5)/(13))=\cos y`

`\cos(\arcsin (5)/(13)) = √(1-\sin^2y)=\sqrt{1-((5)/(13))^2}=\sqrt{1-(25)/(169)}=\sqrt{(144)/(169)}=(12)/(13)`