What is cos ^ -1 ( cos (7 pi/4) )?

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What is cos ^ -1 ( cos (7 pi/4) )?

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Answer 1 · 2015-10-21T00:14:34

$\frac{7 π}{4}$ $(7pi)/4$

Explanation:

$cos$ $cos$ and ${cos}^{- 1}$ $cos^-1$ are effectively just opposite functions of each other. In other words, if $cos (θ) = x$ $cos(theta) = x$ then ${cos}^{- 1} (x) = θ$ $cos^-1(x) = theta$ . That means if you take the ${cos}^{- 1}$ $cos^-1$ of a $cos (θ)$ $cos(theta)$ statement, you just get the original $θ$ $theta$ value back.

${cos}^{- 1} (cos (θ)) = {cos}^{- 1} (x) = θ$ $cos^-1(cos(theta))=cos^-1(x) = theta$

So the given problem simplifies down to $\frac{7 π}{4}$ $(7pi)/4$ , the original $θ$ $theta$ value.

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What is cos ^ -1 ( cos (7 pi/4) )?

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