Question

How do I solve a ) = .8325" alt=" \sin( a ) = .8325" align="absmiddle" class="latex-formula">

It says "Round to the nearest tenth."​

Answer 1

Answer:

$a=56.4\degree$

Step-by-step 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;

$a=56.4\degree$