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

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

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simplify tan(arccos(r/6))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

- t sin (- 3 t) d t

cos^{2} (2 π t) + sin^{2} (2 π t)

f (x) = sec (\frac{1}{4}) x

sec (x) \cdot csc (- tan (x))

- csc (- x)