What is sin(arctan(r/h)) ?

The solution to sin(arctan(r/h)) is (rsqrt(h^2+r^2))/(h^2+r^2)

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simplify sin(arctan(r/h))

simplify

sin (arctan (\frac{r}{h}))

\frac{r h ^{2} + r ^{2}}{h ^{2} + r ^{2}}

Solution steps

sin (arctan (\frac{r}{h}))

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{r}{h} ) 1 + ( \frac{r}{h} ) ^{2}}{1 + ( \frac{r}{h} ) ^{2}}

Simplify

= \frac{r h ^{2} + r ^{2}}{h ^{2} + r ^{2}}

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What is sin(arctan(r/h)) ?
The solution to sin(arctan(r/h)) is (rsqrt(h^2+r^2))/(h^2+r^2)