Periodic function:

A periodic function must have the characteristic of where is the period.

 Horizontal shift of a function:

The graph of is the graph of shifted horizontally by a units.

 Vertical stretching of a function:

The graph of is the graph of stretched vertically by a units.

 Horizontal shrinking of a function:

The graph of is the graph of shrunk horizontally by a units..

 Reflection and vertical shift of a function:

The graph of is the reflection of the graph about x-axis.

The graph of is the graph of shifted vertically by a units.

Sinusoidal functions:

Functions whose equations satisfy .

 Amplitude:

A nonnegative scalar measure of the magnitude of sinusoidal functions.

 Period: For a sinusoidal function  the absolute value of is the period of the  sinusoidal function.

Phase shift of a sinusoidal function:

For a sinusoidal function  the value of  is the phase shift of the sinusoidal function.

Flash Movie	Flash Game	Flash Card
Core Concept Tutorial	Problem Solving Drill	Review Cheat Sheet

This tutorial is all about the graphs of the trigonometric functions.  First, the graphs of sine, cosine, tangent, cotangent, cosecant and secant functions are introduced with the help of examples. Next, equations for a sinusoidal graph are shown in examples with the sine and cosine functions. Properties of sinusoidal functions such as amplitude and period are introduced with graphs and tables.

Next, the transformations of sinusoidal graphs are shown in the examples. The phase shift of a sinusoidal function is defined with a graphical illustration. There are two methodologies to obtain amplitude, period and phase shifts of trigonometric functions. Last, the tangent and the remaining trigonometric equations are defined in terms of their periodicity and amplitude.

Specific Tutorial Features:
• Animated diagrams showing thermal processes
• Graphic organizers to illustrate concept relationships.

Series Features:
• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

The graphs of y=sin(x)
          Periodic functions
          Properties of sin(x)
          Graph transformations
 The graphs of y=cos(x) 
         Properties of cos(x)
  Sinusoidal graphs 
        Graphs of  and  
         Sinusoidal functions
         Amplitude of a sinusoidal function
         Period of a sinusoidal function
         Phase shift of a sinusoidal function
  The graphs of y=tan(x) 
          Properties of tan(x)
          Graph transformations of tan(x)
  The graphs of y=cot(x)
  The graphs of y=csc(x)
  The graphs of y=sec(x)