Question

How do I solve


`\sin( a ) = .8325`

It says "Round to the nearest tenth."​

Answer 1

`a=56.4\degree`

Explanation:

Let
`a` be an acute angle.

To solve:
`\sin(a)=0.8325`, we take the sine inverse of both sides to obtain:

`\sin^(-1)(\sin(a))=\sin^(-1)(0.8325)`

Recall composition property of a function and its inverse function.

`f^(-1)(f(x))=x`

We apply this property to the left hand side to obtain;

`a=\sin^(-1)(0.8325)`

We now use our scientific calculator to obtain;

`a=56.3564115\degree`

We round to the nearest tenth to obtain;

`a=56.4\degree`