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Select the answer which is equivalent to the given expression using your calculator.

cos(arccos ((1)/(sqrt170)))
13

sqrt170

(sqrt170)/(13)

(1)/(sqrt170)

Select the answer which is equivalent to the given expression using your calculator. $\newline$ $\cos \left(\arccos \frac{1}{\sqrt{170}}\right)$ $\newline$ $13$ $\newline$ $\sqrt{170}$ $\newline$ $\frac{\sqrt{170}}{13}$ $\newline$ $\frac{1}{\sqrt{170}}$

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Multiplication with rational exponents

Full solution

Q. Select the answer which is equivalent to the given expression using your calculator.

\newline

\cos \left(\arccos \frac{1}{\sqrt{170}}\right)

\newline

13

\newline

\sqrt{170}

\newline

\frac{\sqrt{170}}{13}

\newline

\frac{1}{\sqrt{170}}

Recognize Functions Cancel Out: We are given the expression $\cos(\arccos(\frac{1}{\sqrt{170}}))$ . The $\arccos$ function is the inverse of the cosine function, which means that $\arccos(\cos(x)) = x$ for any value of $x$ within the domain of the cosine function. Therefore, we can simplify the expression by recognizing that the cosine and arccosine functions will cancel each other out.
Use Inverse Function: Since $\text{arccos}$ is the inverse of $\cos$ , we have: $\newline$ $\cos(\text{arccos}(\frac{1}{\sqrt{170}})) = \frac{1}{\sqrt{170}}$ $\newline$ This is because $\text{arccos}(\frac{1}{\sqrt{170}})$ will give us an angle whose cosine is $\frac{1}{\sqrt{170}}$ , and taking the cosine of that angle will return us to the original value of $\frac{1}{\sqrt{170}}$ .
Simplify Further: We do not need a calculator to simplify this expression further, as we have already found that the cosine and arccosine functions cancel each other out, leaving us with the original value inside the arccos function.

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