To graph the tangent function, we mark the angle along the horizontal x axis, and for each angle, we put the tangent of that angle on the vertical y-axis. The result, as seen below, is rather jagged curve that goes to positive infinity in one direction and negative infinity in the other. You can find the tangent of any angle, no matter how large, with one exception. If you look at the graph below you see that tan 90° is undefined, because it requires dividing by zero. Therefore, angles like this are not in the domain of the tan functions and produce an undefined result.
Drag the red dot and see the values obtained by the tangent function. Check that the period of the tangent function is `pi`.
You know how to graph many types of functions. Graphs are useful because they can take complicated information and display it in a simple, easy-to-read manner. The graphs of trigonometric functions have several properties to elicit (Amplitude, Interval, Period, Horizontal Shift, Vertical Shift). To be able to graph these functions by hand, we have to understand them. Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. But you still need to remember what they mean!