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Using the standard domain for the sine function, which of the following expressions corresponds to the composite function sin(accosx)?

Using the standard domain for the sine function, which of the following expressions-example-1
User PKlumpp
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1 Answer

9 votes
9 votes

Step-by-step explanation:

We are given the composite function;


sin(arccosx)

We are required to determine the expression that corresponds to this.

To do that, we shall recall the Pythagorean identity, and that is;


sin^2\theta+cos^2\theta=1
\begin{gathered} If\text{ }\theta=arccos(x) \\ Then\text{ }\theta\text{ }\in[0,\pi] \end{gathered}

And;


sin\theta\ge0

Therefore;


sin(arccos(x))=sin\theta

Going back to our Pythagorean identity;


\begin{gathered} sin^2\theta+cos^2\theta=1 \\ sin^2\theta=1-cos^2\theta \end{gathered}

Take the square root of both sides;


sin\theta=√(1-cos^2\theta)

Where you have;


\theta=arccos(x)
sin(arccos(x))=√(1-x^2)

ANSWER:

Option D:


√(1-x^2)

User Nelga
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