What is the general solution for solvefor y,x+arctan(y/x)=0 ?

The general solution for solvefor y,x+arctan(y/x)=0 is y=tan(-x)x

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solvefor y,x+arctan(y/x)=0

solve for

y, x + arctan (\frac{y}{x}) = 0

y = tan (- x) x

Solution steps

x + arctan (\frac{y}{x}) = 0

Solve by substitution

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

Solve by substitution

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

Let:

u = \frac{y}{x}

x + arctan (u) = 0

Move

x

to the right side

arctan (u) = - x

Apply trig inverse properties

u = tan (- x)

Substitute back

u = \frac{y}{x}

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

y = tan (- x) x

sin (45 + 2 α) = \frac{3}{2}

θ, 2 sin (θ) - 5 = 0

(tan (x) - 3) (2 sin (x) - 1) = 0

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

2 sin^{2} (x) - 5 sin (x) - 4 = 0

What is the general solution for solvefor y,x+arctan(y/x)=0 ?
The general solution for solvefor y,x+arctan(y/x)=0 is y=tan(-x)x