How do you simplify the expression $sin (arccos (\frac{1}{2}))$ $sin(arccos(1/2))$ ?

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How do you simplify the expression $sin (arccos (\frac{1}{2}))$ $sin(arccos(1/2))$ ?

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Answer 1 · 2016-06-11T12:23:51

$\frac{\sqrt{3}}{2}$ $sqrt3/2$

Explanation:

$arccos x \equiv {cos}^{- 1} x$ $arccos x -= cos^-1 x$
Given expression is
$sin (arccos (\frac{1}{2}))$ $sin(arccos (1/2))$
$= sin ({cos}^{- 1} (\frac{1}{2}))$ $=sin(cos^-1 (1/2))$
or $sin (60^{\circ})$ $sin(60^@)$
or $\frac{\sqrt{3}}{2}$ $sqrt3/2$

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How do you simplify the expression $sin (arccos (\frac{1}{2}))$ $sin(arccos(1/2))$ ?

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How do you simplify the expression $sin (arccos (\frac{1}{2}))$ $sin(arccos(1/2))$ ?