Precalculus: Basic Trigonometric Transformations

Objectives

• Students will identity the amplitude, period, horizontal shift, and vertical shift in the equation and the effect that these parameters have upon the graph of the function.
• Students will discover that the horizontal shift of a sinusoidal function is determined by the quotient of two of the parameters of the function.
• Students will utilize their knowledge of the effect of the parameters of a sine function to rewrite its equation as an equation containing a cosine function.
• Students will write equations for sine and cosine functions by examining their parameters and looking at their graphs.

Vocabulary

• amplitude
• horizontal shift
• parameters
• period
• phase shift
• vertical shift

About the Lesson

This lesson involves manipulating sliders to change the values of parameters in trigonometric functions and determining the effect that each change has upon the shape of the graph.

As a result, students will:

• Examine graphs and information about parameters of functions to write equations of sine and cosine functions.
• Incorporate their knowledge of the effect of parameters to rewrite the equation of a sine function in terms of a cosine function.
• Understand the effect that each of the parameters has on the graph of a function.
• Understand how two of the parameters of a sinusoidal function effect its horizontal shift.
• Know how to rewrite the equation of a sine function as an equation containing a cosine function.