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

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

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simplify sin(arctan(x/y))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

sin (36 0^{\circ} + x)

sin (x + 3 0^{\circ})

tan (9 0^{\circ} - a)

sin (arccos (\frac{x}{4}))

tan (9 0^{\circ} + a)

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