Sullivan Algebra and Trigonometry: Section 7.6 Objectives of this Section Graph Transformations of the Sine Function Graph Transformations of the Cosine Function Determine the Amplitude and Period of Sinusoidal Functions Graph Sinusoidal Functions: y = Asin(wx) Find an Equation for a Sinusoidal Graph
The Graph of y = sin x y x
(0, 0)
Characteristics of the Sine Function 1. The domain is the set of all real numbers. 2. The range consists of all real numbers from -1 to 1, inclusive. 3. The sine function is an odd function (symmetric with respect to the origin).
Characteristics of the Sine Function
Begin with the basic sine function: (0, 0)
The Graph of y = cos x y x
(0, 1)
Characteristics of the Cosine Function 1. The domain is the set of all real numbers. 2. The range consists of all real numbers from -1 to 1, inclusive. 3. The cosine function is an even function (symmetric with respect to the y-axis).
Characteristics of the Cosine Function
The graphs of the sine and cosine functions are called sinusoidal graphs.
1 -1
2 -2
Find an equation for the graph. 4 3 2 -1 1 -4