What is sin(arccos(y/2)) ?

The solution to sin(arccos(y/2)) is (sqrt(4-y^2))/2

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simplify sin(arccos(y/2))

simplify

sin (arccos (\frac{y}{2}))

\frac{4 - y ^{2}}{2}

Solution steps

sin (arccos (\frac{y}{2}))

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (\frac{y}{2})^{2}

Simplify

= \frac{4 - y ^{2}}{2}

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