How do I find all the solutions for tan(x)=k?

[Al-Layth]

I am doing a problem where I had to solve an equation of the form
[math]\tan(x)=k [/math]
[math]-2\pi\leq x \leq 2\pi[/math]
but the Problem wants multiple solutions. My calculator only gave one.
What are the general methods of finding all solutions to
[math]\tan(x)=k[/math] in the domain I mentioned??

 

[Dr.Peterson]

I am doing a problem where I had to solve an equation of the form
[math]\tan(x)=k [/math]
[math]-2\pi\leq x \leq 2\pi[/math]
but the Problem wants multiple solutions. My calculator only gave one.
What are the general methods of finding all solutions to
[math]\tan(x)=k[/math] in the domain I mentioned??

The inverse tangent function gives you the one angle in [imath](-\frac{\pi}{2},\frac{\pi}{2})[/imath].

There are others in the given domain. Find them!

Think of what you know about quadrants and reference angles, perhaps. Or think about the graph of the tangent function. Or about the period of the function. There are several ways to use what you know.