How do you evaluate ${cos}^{- 1} (cos (\frac{π}{6}))$ $cos^-1(cos(pi/6))$ without a calculator?

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How do you evaluate ${cos}^{- 1} (cos (\frac{π}{6}))$ $cos^-1(cos(pi/6))$ without a calculator?

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Answer 1 · 2016-09-05T16:23:35

${cos}^{- 1} (cos (\frac{π}{6})) = \frac{π}{6}$ $cos^-1(cos(pi/6))=pi/6$ .

Explanation:

The Defn. of ${cos}^{- 1}$ $cos^-1$ fun. :

${cos}^{- 1} x = θ, | x | \leq 1 \Leftrightarrow x = cos θ, θ \in [0, π]$ $cos^-1 x=theta, |x|le1 iff x=cos theta, theta in [0,pi]$ .

Sub.ing the value of $x$ $x$ , we have,

${cos}^{- 1} (cos θ) = θ, θ \in [0, π]$ $cos^-1(cos theta)=theta, theta in [0,pi]$ .

In our case, since, $θ = \frac{π}{6} \in [0, π], we get, {cos}^{- 1} (cos (\frac{π}{6})) = \frac{π}{6}$ $theta=pi/6 in [0,pi]", we get, "cos^-1(cos(pi/6))=pi/6$ .

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How do you evaluate ${cos}^{- 1} (cos (\frac{π}{6}))$ $cos^-1(cos(pi/6))$ without a calculator?

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Explanation:

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How do you evaluate ${cos}^{- 1} (cos (\frac{π}{6}))$ $cos^-1(cos(pi/6))$ without a calculator?