What is the general solution for solvefor x,u=arctan(x/y) ?

The general solution for solvefor x,u=arctan(x/y) is x=tan(u)y

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solvefor x,u=arctan(x/y)

solve for

x, u = arctan (\frac{x}{y})

x = tan (u) y

Solution steps

u = arctan (\frac{x}{y})

Switch sides

arctan (\frac{x}{y}) = u

Subtract

u

from both sides

arctan (\frac{x}{y}) - u = 0

Solve by substitution

arctan (\frac{x}{y}) = u

Let:

v = \frac{x}{y}

arctan (v) - u = 0

Move

u

to the right side

arctan (v) = u

Apply trig inverse properties

v = tan (u)

Substitute back

v = \frac{x}{y}

\frac{x}{y} = tan (u) : x = tan (u) y; y \neq = 0

x = tan (u) y

4 cos^{2} (2 x - 1) = 1

sin^{2} (x) - 2 cos^{2} (x) + cos^{2} (x) = 0

3 \cdot sin (x) = cos (x)

sin^{22} (x) sin^{3} (x) + 6 = 18

d^{2} + 4 d + 4 = sin (x)

What is the general solution for solvefor x,u=arctan(x/y) ?
The general solution for solvefor x,u=arctan(x/y) is x=tan(u)y