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

Related Topics:
More Lessons for Trigonometry
Math Worksheets

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)

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

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 