1 Answer

Gansub · Answer 1 · 2023-12-08T16:14:19+0000

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

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