How do you evaluate ${cos}^{- 1} (cos (\frac{π}{10}))$ $cos^-1(cos((pi)/10))$ ?

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How do you evaluate ${cos}^{- 1} (cos (\frac{π}{10}))$ $cos^-1(cos((pi)/10))$ ?

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Answer 1 · 2016-12-12T13:33:54

The answer is $\frac{π}{10}$ $pi/10$

Explanation:

By definition, ${cos}^{- 1} (x)$ $cos^(-1)(x)$ is an angle $ϕ$ $phi$ that satisfies two requirements:

(1) $cos ϕ = x$ $cos phi = x$ (the main part of a definition)

(2) $0 \leq ϕ \leq π$ $0<=phi<=pi$ (to assure uniqueness of the result)

In our case $x = cos (\frac{π}{10})$ $x=cos(pi/10)$ , so the first requirement is $cos (ϕ) = cos (\frac{π}{10})$ $cos(phi)=cos(pi/10)$ and the obvious candidate for $ϕ$ $phi$ is $\frac{π}{10}$ $pi/10$ .

For this $ϕ = \frac{π}{10}$ $phi=pi/10$ the second requirement is held.

Therefore, the answer is $\frac{π}{10}$ $pi/10$ .

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How do you evaluate ${cos}^{- 1} (cos (\frac{π}{10}))$ $cos^-1(cos((pi)/10))$ ?

1 Answer

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