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How to Determine the Shift in a Cosine Function

The cosine is a trigonometric function. Like all trigonometric functions, the cosine is periodic. That is, it repeats in a cycle. If the angle is measured in degrees, then the cos(x + a*360) = cos(x) where "a" is a constant. For example, cos(100) = -0.17, and cos(460) =-0.17. The shift in a cosine might be vertical or horizontal. The horizontal shift is also known as phase shift.

Things You'll Need

A graph of a shifted cosine function, with angle on the horizontal axis and the cosine of the angle on the vertical axis.

Instructions

- 1
  Find the maximum of the cosine -- that is, the highest point on the curve.
- 2
  Draw a straight line from that point to the y-axis (the vertical one). Note the value where the line crosses the axis.This value is the vertical shift. For example, if the highest point of the curve is at 2.5, then the vertical shift is 2.5.
- 3
  Draw a straight line from the highest point to the x-axis and note the value where the line crosses the axis.
- 4
  Find the difference between this value and 360 degrees. For example, if the line crosses the x-axis at 180 degrees, the horizontal shift is 180 degrees. Because of the cyclical nature of the cosine function, the phase shift can always be expressed as a positive number.

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