If $sin x = \frac{4}{5}$ $sinx=4/5$ what is the value of $cos x$ $cosx$ ?

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If $sin x = \frac{4}{5}$ $sinx=4/5$ what is the value of $cos x$ $cosx$ ?

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Answer 1 · 2016-02-16T06:24:24

$cos x = + (\frac{3}{5}) or - (\frac{3}{5})$ $cosx=+(3/5) or -(3/5)$

Explanation:

Recall trigonometric identity ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2x+cos^2x=1$ . Hence ${cos}^{2} x = 1 - {sin}^{2} x$ $cos^2x=1-sin^2x$ or

$cos x = \sqrt{1 - {sin}^{2} x} = \sqrt{1 - {(\frac{4}{5})}^{2}} = \sqrt{1 - \frac{16}{25}} = \sqrt{\frac{9}{25}}$ $cosx=sqrt(1-sin^2x)=sqrt(1-(4/5)^2)=sqrt(1-16/25)=sqrt(9/25)$

i.e. $cos x = + (\frac{3}{5}) or - (\frac{3}{5})$ $cosx=+(3/5) or -(3/5)$

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Explanation:

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