First off, I’m assuming that your calculator has three things: a “tan” button and a “tan-1” button. You do not have to know where the “tan-1” button is, but if it is a scientific calculator then it probably does have it. I’m also assuming that you know what the “tan” and the “tan-1” buttons do, so this will not explain that.
Your calculator should have a button labeled “tan-1”, although usually you have to hit the “2nd” key and then the “tan” key. If you are using the calculator that comes installed with Windows 7 (at least I’m pretty sure that’s where it comes from, if someone could verify that please) and already have it set to scientific calculator (hit the “view” button in the top left corner then select “scientific”), then you hit the “Inv” key (short for “Inverse”, I think) and the “tan” button will turn into “tan-1”.
Also, make sure that the calculator is set to degrees (or radians), because it is extremely frustrating to get the wrong answer and have no idea why. To set that there is often a button that says “DRG”, with which you can cycle through degrees, radians, and gradients, using arrow keys if your calculator has them. On the Windows 7 calculator there are three buttons in the top left, beneath where the output is shown. Click the one labeled with what you want.
Finally, if you already know how to get the “tan-1” button but don’t know how to type it in, most fancy calculators (the $10+ ones) require you to input the items in the order that you would write them (e.g. type “tan-1” then “500” then “/” then “1001” then “=”). However, almost every other calculator that I use (including the Windows 7 one and calculator apps) do it similarly, but certain functions (such as square root, log, and tan) are done after you finish typing the expression (e.g. type “500” then “/” then “1001” then “tan-1” then “=”).
Of course, all of this also applies to the “sin”/”sin-1” and “cos”/”cos-1” buttons, but I was specifically asked about the “tan-1” button, so that’s what I went with.