Question

Question #02358

Answer 1

Please see the explanation.

Explanation:

Any point on the `x = 0` line is a trivial solution.

Let's find an equation for y in terms of x for values of `x !=0`.

Subtract x from both sides of the equation:

`tan(xy) = -x`

Use the inverse tangent function on both sides:

`tan^-1(tan(xy)) = tan^-1(-x)`

The left side becomes xy, due to a property of a function and its inverse:

`xy = tan^-1(-x)`

Divide both sides of the equation by x:

`y = tan^-1(-x)/x; x!=0" [1]"`

This is the equation for all values x except 0

Here is a graph of all of the possible solutions:

The blue line is all of the possible values of y, when `x = 0`
The red line is all of the possible values of y as a function of x except 0.