Section 3-2 General Sinusoidal Graphs “I have done my best.” That is about all the philosophy of living that one needs. - Lin-yutang

Definition: General Sinusoidal Equation Or Is the amplitude (A is the vertical dilation, which can be positive or negative) B is the reciprocal of the horizontal dilation C is the location of the sinusoidal axis (vertical translation) D is the phase displacement (horizontal translation)

Property: Period and Frequency of a Sinusoid For general equations Or So And

Concavity, Points of Inflection, and Upper and Lower Bounds High points and low points are called critical points.

Example: Suppose that a sinusoid has a period of 150 per cycle, an amplitude of 8 units, a phase displacement of -60 with respect to the parent cosine function, and a sinusoidal axis 3 units below the q-axis. Without using your grapher, sketch this sinusoid and then find an equation for it.

Example For the sinusoid below, give the period, frequency, amplitude, phase displacement and sinusoidal axis location. Write a particular equation of the sinusoid.

Example The figure below shows a quarter-cycle of a sinusoid. Write a particular equation for the figure.