How do you simplify $sin ({cos}^{- 1} (- \frac{1}{4}))$ $sin (cos^-1 (-1/4))$ ?

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Answer 1 · 2018-05-06T05:59:02

The answer is $= \pm \frac{\sqrt{15}}{4}$ $=+-sqrt15/4$

Let $x = {cos}^{- 1} (\frac{1}{4})$ $x=cos^-1(1/4)$

Then,

$cos x = \frac{1}{4}$ $cosx=1/4$

Therefore,

$sin ({cos}^{- 1} (\frac{1}{4})) = sin x$ $sin(cos^-1(1/4))=sinx$

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

$sin x = \pm \sqrt{1 - {cos}^{2} x}$ $sinx=+-sqrt(1-cos^2x)$

$= \pm \sqrt{1 - \frac{1}{16}}$ $=+-sqrt(1-1/16)$

$= \pm \frac{\sqrt{15}}{4}$ $=+-sqrt15/4$

How do you simplify sin (cos^-1 (-1/4))sin(cos−1(−14))sin (cos^-1 (-1/4))?