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

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

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solvefor x,z=arctan(x/y)

solve for

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

x = tan (z) y

Solution steps

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

Switch sides

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

Subtract

z

from both sides

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

Solve by substitution

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

Let:

u = \frac{x}{y}

arctan (u) - z = 0

Move

z

to the right side

arctan (u) = z

Apply trig inverse properties

u = tan (z)

Substitute back

u = \frac{x}{y}

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

x = tan (z) y

- \frac{1}{2} = cos (θ)

4 cos^{2} (x) - 3 cos (x) - 2 = 0

sin (x) = cos (3 x)

x, y = 5 sin (\frac{x}{4})

3 sin (\frac{π}{3} x) = 2

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