This lesson involves examining graphs, or partial graphs, of sinusoidal functions to determine the values of their parameters and to express them in various ways involving sine and cosine functions.

• Students will understand the effect that each of the parameters A, B, C, and D has on the graph of a sinusoidal function of the form y = ±A sin (B(x - C)) + D or y = ±A cos (B(x - C)) + D.
• Students will understand that sinusoidal functions can be expressed in a variety of equivalent forms.

• amplitude
• cycle
• horizontal shift
• parameters
• period
• vertical shift

This lesson involves examining graphs, or partial graphs, of sinusoidal functions to determine the values of their parameters and to express them in various ways involving sine and cosine functions

As a result, students will:

• Write the equation for each graph in the forms y = ±A sin (B(x - C)) + D or y = ±A cos (B(x - C)) + D.
• Rewrite functions f(x) = A sin (Bx) + C sin (Dx) to the form where M is a positive integer.
• Analyze graphs and verify their rewritten functions using algebra and “trig identities.”