Question #02358

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Answer 1 · 2017-01-25T16:17:26

Please see the 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:

![Desmos.com]( useruploads.socratic.org )

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.