Return to the Purplemath home page

 The Purplemath Forums
Helping students gain understanding
and self-confidence in algebra

powered by FreeFind


Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

Graphing Trig Functions: Phase Shift (page 3 of 3)

Sections: Introduction, Examples with amplitude and vertical shift, Example with phase shift

  • Graph two periods of g(x) = sinx + π/2) + 3
  • The amplitide is going to be the same, but the midline of the graph is going to be at y = 3 instead of y = 0 (that is, the x-axis). The period is going to be (2π)/(π) = 2. The argument factors as π(x + 1/2), so the graph will be shifted 1/2 unit to the left.

    I'll do the usual graph: Copyright Elizabeth Stapel 2010-2011 All Rights Reserved

      graph of sin(x) from 0 to 4pi

    Instead of shifting the sine wave three units up, I'll shift the horizontal axis three units down, and re-number the y-axis:

      same graph, but with horizontal axis shifted downward by three units, and y-axis re-numbered

    The regular period goes from 0 to ; this one goes from 0 to 2, so I'll re-number the x-axis:

      same graph, but with x-axis labelled 0, 1, 2, 3, 4 instead of 0, pi, 2pi, 3pi, 4pi

    And the graph is shifted to the left by 1/2, so I'll shift the y-axis to the right by 1/2  and re-number the x-axis a bit more:

      same sine wave, but with y-axis shifted one-half unit to the right, and the x-axis re-numbered

Can you see why I used pencil and did a lot of erasing when I was doing graphing?

My best advice regarding doing these graphs is to practice, practice, practice. You don't want to freeze or have a "brain-fart" on the test, and this is pretty straightforward, once you get the feel of it. So keep doing extra graphing, until you are feeling comfortable and confident in your skills.

<< Previous  Top  |  1 | 2 | 3  |  Return to Index

Cite this article as:

Stapel, Elizabeth. "Graphing Trig Functions: Phase Shift." Purplemath. Available from Accessed


  Linking to this site
  Printing pages
  School licensing

Reviews of
Internet Sites:
   Free Help
   Et Cetera

The "Homework

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor

This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2010-2012  Elizabeth Stapel   |   About   |   Terms of Use


 Feedback   |   Error?