This section discusses the graph of the tangent function (shown below).
For ease of reference, some material is repeated
from the Trigonometric Functions.
Recall that every real number is uniquely defined by its sign (plus or minus) and its size (distance from zero).
Sign of the Tangent FunctionThe sign of $\,\tan t\,$ is easily determined from its definition as $\,\displaystyle\frac{\sin t}{\cos t}\,$:

Sign of the Tangent Function 
Size of the Tangent FunctionThe size of the tangent is best understood from its graphical significancein the unit circle approach, as follows:

Size of the Tangent Function Variations in Length of the Tangent Segment Size of the Tangent Function 
There is an additional
insight that comes from studying the diagram at right:


On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
