What is sin(arctan(3x)) ?

The solution to sin(arctan(3x)) is (3xsqrt(1+9x^2))/(1+9x^2)

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simplify sin(arctan(3x))

simplify

sin (arctan (3 x))

\frac{3 x 1 + 9 x ^{2}}{1 + 9 x ^{2}}

Solution steps

sin (arctan (3 x))

Use the following identity:

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

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

Simplify

= \frac{3 x 1 + 9 x ^{2}}{1 + 9 x ^{2}}

cos (kπ)

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

sin (arcsin (y))

cos (θ + \frac{π}{2})

cos (x - 18 0^{\circ})

What is sin(arctan(3x)) ?
The solution to sin(arctan(3x)) is (3xsqrt(1+9x^2))/(1+9x^2)