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

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

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simplify sin(arctan(y/x))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cos (18 0^{\circ} - θ)

sin (arctan (\frac{x}{2}))

sec (arcsin (x))

cos (- 2 x)

cos (\frac{3 π}{2} + x)

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