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

The solution to sin(arctan(x/3)) is (xsqrt(9+x^2))/(9+x^2)

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simplify sin(arctan(x/3))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

sin (18 0^{\circ} + x)

sin (tan (- 1 (x)))

tan (arcsin (\frac{x}{2}))

tan (arcsin (\frac{x}{3}))

cos (arcsin (\frac{7}{x}))

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