What is sin(arctan(x/9)) ?

The solution to sin(arctan(x/9)) is (xsqrt(81+x^2))/(81+x^2)

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simplify sin(arctan(x/9))

simplify

sin (arctan (\frac{x}{9}))

\frac{x 81 + x ^{2}}{81 + x ^{2}}

Solution steps

sin (arctan (\frac{x}{9}))

Use the following identity:

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

= \frac{( \frac{x}{9} ) 1 + ( \frac{x}{9} ) ^{2}}{1 + ( \frac{x}{9} ) ^{2}}

Simplify

= \frac{x 81 + x ^{2}}{81 + x ^{2}}

tan (arcsin (\frac{x}{a}))

sin (9 0^{\circ} - \frac{x}{2})

16 - (4 sin (θ))^{2}

csc (arccos (u))

cot (x - π)

What is sin(arctan(x/9)) ?
The solution to sin(arctan(x/9)) is (xsqrt(81+x^2))/(81+x^2)