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