How do you calculate $cos [Sin^-1 (-1/5) ]$ ?

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How do you calculate $cos [Sin^-1 (-1/5) ]$ ?

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Answer 1 · 2015-04-30T18:49:52

In this way:

we have to calculate $cosalpha$ , where

$alpha=sin^-1(-1/5)$ ,

$sinalpha=-1/5$ .

Since the range of the function $y=sin^-1x$ is an angle in the first and fourth quadrant, and since the value is negative, the angle $alpha$ is in the fourth quadrant, and there the function cosine is positive, so:

$cosalpha=+sqrt(1-sin^2alpha)=sqrt(1-1/25)=sqrt(24/25)=2/5sqrt6$ .

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How do you calculate $cos [Sin^-1 (-1/5) ]$ ?

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