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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.

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Cite this article as:

Stapel, Elizabeth. "Graphing Trig Functions: Phase Shift." Purplemath. Available from
    http://www.purplemath.com/modules/grphtrig3.htm. Accessed
 

 



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