What is tan(arccos(y/6)) ?

The solution to tan(arccos(y/6)) is (sqrt(36-y^2))/y

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simplify tan(arccos(y/6))

simplify

tan (arccos (\frac{y}{6}))

\frac{36 - y ^{2}}{y}

Solution steps

tan (arccos (\frac{y}{6}))

Use the following identity:

tan (arccos (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( \frac{y}{6} ) ^{2}}{( \frac{y}{6} )}

Simplify

= \frac{36 - y ^{2}}{y}

sin (x + \frac{π}{6})

cos (arcsin (5 x))

csc (arctan (x - 2))

cos (n \cdot π)

sin (θ + \frac{π}{2})