How do you simplify $sin (cos^-1 (-1/4))$ ?

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Answer 1 · 2018-05-06T05:59:02

The answer is $=+-sqrt15/4$

Let $x=cos^-1(1/4)$

Then,

$cosx=1/4$

Therefore,

$sin(cos^-1(1/4))=sinx$

$sin^2x+cos^2x=1$

$sinx=+-sqrt(1-cos^2x)$

$=+-sqrt(1-1/16)$

$=+-sqrt15/4$

How do you simplify sin (cos^-1 (-1/4))sin (cos^-1 (-1/4))?