Start with the function
f(x) = tan x
Or
y = tan x
Put your angles on the x-axis, and the values of the tangent on the y-axis.
You can use degrees or radians on your x-axis.
Choose values for x.
Find corresponding values for y.
Use you calculator, making sure that you are set to either degrees or radians, whichever you chose for your graph.
Graph those (x,y) points and you will see graph of the tangent function begin to emerge.
For angle values of x that give you an undefined answer, you are seeing the vertical asymptotes of the tangent function. Moving left to right, as the function approaches those asymptotes, the values go to positive infinity. Moving to the right away from the asymptotes, the tangent comes up from negative infinity.
You will soon see that the graph repeats every 180 degrees (or every pi radians). We say that the "period" of the tangent function is 180 degrees.
Remember that the pattern of your repeating graph continues to the left into the negative angle values as well.
Check your answer by typing
y = tan x into a graphing utility, such as desmos.com.
