What is sin(arctan(u/3)) ?

The solution to sin(arctan(u/3)) is (usqrt(9+u^2))/(9+u^2)

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simplify sin(arctan(u/3))

simplify

sin (arctan (\frac{u}{3}))

\frac{u 9 + u ^{2}}{9 + u ^{2}}

Solution steps

sin (arctan (\frac{u}{3}))

Use the following identity:

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

= \frac{( \frac{u}{3} ) 1 + ( \frac{u}{3} ) ^{2}}{1 + ( \frac{u}{3} ) ^{2}}

Simplify

= \frac{u 9 + u ^{2}}{9 + u ^{2}}

- sin (9 t + 2 π) - 4 sin (- 9 t)

sin^{2} (x + \frac{π}{2})

9 sec^{2} (x) - 9

sin (- 3 θ)

- cos (x + \frac{π}{6})

What is sin(arctan(u/3)) ?
The solution to sin(arctan(u/3)) is (usqrt(9+u^2))/(9+u^2)