What Does the Graph of the Tangent Function Look Like?

Note:

If you want to make the graph of the tangent function, you can use the unit circle to help you plot points. This tutorial shows you how to use the unit circle to make the tangent function graph!

Keywords:

definition
tangent
graph
derive
plot
coordinate plane
radian
trigonometry

Background Tutorials

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.
- What is a Multiple?
  
  Being able to find multiples of a number is important, especially if you want to find the least common multiple (LCM) between numbers. In this tutorial, you'll be introduced to the term multiple. You'll also see how to find multiples of a given number!
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the Coordinate Plane?
  
  You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
- Why Can't You Divide By 0?
  
  Why can't you divide by 0? This may be one of the most asked math questions. Get this question answered once and for all by watching this tutorial!
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- What is Domain?
  
  Did you know that a relation has a domain? The domain of a relation is the set of the first coordinates from the ordered pairs. This tutorial defines the domain of a relation!
- What is the Range of a Relation?
  
  Did you know that a relation has a range? The range of a relation is the set of the second coordinates from the ordered pairs. This tutorial defines the range of a relation!
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- What is a Periodic Function?
  
  Periodic functions have some special qualities! In this tutorial, you'll be introduced to these functions and learn what a graph must have to be called a periodic function.
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
- What is an Angle in Standard Position?
  
  Understanding how angles are made in the coordinate plane is a big step towards understanding trigonometry. This tutorial shows you how an angle can be made in the coordinate plane!