The graphs of
sine and cosine are the same when sine is shifted
left by  .
Such a horizontal shifting is called a phase
shift.
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phase shift: |
Phase shift is the measure of horizontal shifting. If the phase shift is positive, the horizontal shift is to the right. If the phase shift is negative, the horizontal shift is to the left.
The easiest way to determine phase shift is to determine by how many units the "starting point" (0,0) of a standard sine curve, y = sin(x), has moved to the right or left. |
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Be careful here!! When
trying to determine the direction of a phase shift, be sure you have the
function in the proper form,
. (Notice
the
subtraction
of C.)
The phase shift is determined by the value of
C.
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This expression is really
 where the value
of C is negative and the shift is left. |
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In this expression the value of C is positive and the shift is right. |
Another BEWARE!!!
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What is the phase shift of
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At first glance, it may seem that the phase shift is
 , but it is
NOT. The phase shift is actually
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?
, because the
equation is actually
Phase shifts can be applied to all trigonometric functions.
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