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Graphs of Trigonometric Functions

 Topic Review on "Title": 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.

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 "Title" Tutorial Summary : This tutorial discussed the graphs of trigonometric functions. Sine, cosine, tangent, cotangent, cosecant and secant function graphs are introduced with the help of examples and visuals. Equations for a sinusoidal graph are shown in examples using sine and cosine related functions. Properties of sinusoidal functions such as amplitude and period are introduced with graphs and tables. Transformations of sinusoidal graphs are shown to emphasize their use and importance in applications such as in physics. 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. The tangent and the remaining trigonometric equations are defined in terms of their periodicity and amplitude.

 Tutorial Features: Specific Tutorial Features: • Animated graphs showing the different types of trigonometric functions • 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.

 "Title" Topic List: The graphs of y= sin(x) Periodic functions Properties of y= sin(x) Graph transformations The graphs of y= cos(x) Properties of y= cos(x) Sinusoidal graphs Graphs of sin(x) and cos(x-0.5pi) 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 y=tan(x) Graph transformations of y=tan(x) The graphs of y=cot(x) The graphs of y=csc(x) The graphs of y=sec(x)

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