What is $cos ({sin}^{- 1} (0.5))$ $cos(sin^-1(0.5))$ ?

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What is $cos ({sin}^{- 1} (0.5))$ $cos(sin^-1(0.5))$ ?

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Answer 1 · 2018-04-13T01:19:55

$cos ({sin}^{- 1} (0.5)) = \frac{\sqrt{3}}{2}$ $cos(sin^(-1)(0.5))=sqrt(3)/2$

Explanation:

Let ${sin}^{- 1} (0.5) = x$ $sin^(-1)(0.5)=x$ then

$\to sin x = 0.5$ $rarrsinx=0.5$

$\to cos x = \sqrt{1 - {sin}^{2} x} = \sqrt{1 - {0.5}^{2}} = \sqrt{1 - {(\frac{1}{2})}^{2}} = \frac{\sqrt{3}}{2}$ $rarrcosx=sqrt(1-sin^2x)=sqrt(1-0.5^2)=sqrt(1-(1/2)^2)=sqrt(3)/2$

$\to x = {cos}^{- 1} (\frac{\sqrt{3}}{2}) = {sin}^{- 1} (0.5)$ $rarrx=cos^(-1)(sqrt3/2)=sin^(-1)(0.5)$

Now,

$\to cos ({sin}^{- 1} (0.5)) = cos ({cos}^{- 1} (\frac{\sqrt{3}}{2})) = \frac{\sqrt{3}}{2}$ $rarrcos(sin^(-1)(0.5))=cos(cos^(-1)(sqrt3/2))=sqrt(3)/2$

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What is $cos ({sin}^{- 1} (0.5))$ $cos(sin^-1(0.5))$ ?

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