Graphing Trig Functions: Amplitude, Period, Vertical and Horizontal Shifts

In this lesson we will look at Graphing Trig Functions: Amplitude, Period, Vertical and Horizontal Shifts.

Graphing Sine and Cosine with Phase (Horizontal) Shifts
How to find the phase shift (the horizontal shift) of a couple of trig functions?
Example:
What is the phase shift for each of the following functions?

1. y = cos(x - 4)
   
2. y = sin [2(x + 1)]
   
3. y = cos (10x + 30)

Graphing Sine and Cosine with Phase (Horizontal) Shifts
How to graph a trigonometric function by graphing the original and then applying the phase shift?
Example:
Which graph most closely resembles the graph of y = -2 sin (x - π)

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Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts
How to find the amplitude, period, vertical and horizontal shifts for a trig function and use that to graph the function.
Example:
Graph y = 2 cos(x - π/2) + 1

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