Training Camp (cont 9)

The following summarizes the key characteristics of the equation of a sinusoidal function.

Any sinusoidal function can be expressed as either a sine function or a cosine function. A sinusoidal function of the form y = a sin b(x – c) + d or y = a cos b(x – c) + d has the following characteristics:

• The value of a is the amplitude.

• The value of b is the number of cycles in 360° or 2π radians.

• The period is .

• The value of c indicates the horizontal translation that has been applied to the graph of y = sin x or y = cos x.

• The equation of the midline is y = d where .

• The maximum value is d + a and the minimum value is d – a.

• The graph below represents a sine curve. In the graph of a cosine curve, c is the distance from the y-axis to the first maximum point.

In this Training Camp, you have identified the key characteristics of a sinusoidal function. Now, you will use these characteristics to match the graph of a sinusoidal function to its corresponding equation.