Question

I need help solving this problem I’m struggling to answer it. It is trigonometry and it is from my ACT prep guide

Answer 1

The Solution:

Given the value below:

$\cos \lbrack\sin ^{-1}(-0.845)\rbrack$

We are asked to find the value of the above expression rounded to the nearest thousandth.

So, applying the property rule:

$\sin ^{-1}(-x)=-\sin ^{-1}(x)$

We have that:

$\sin ^{-1}(-0.845)=-\sin ^{-1}(0.845)=-57.671936$

So, it follows that:

$\cos \lbrack\sin ^{-1}(-0.845)\rbrack=\cos (-57.671936)$

Applying the property rule:

$\cos (-x)=\cos (x_{})$

We have that:

$\cos \lbrack\sin ^{-1}(-0.845)\rbrack=\cos (-57.671936)=\cos (57.671936)=0.534766$

Rounding to the nearest thousandth, we get

$\cos \lbrack\sin ^{-1}(-0.845)\rbrack=\cos (-57.671936)=0.534766\approx0.535$

Therefore, the correct answer is 0.535