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How to Graph an Inverse Cosine Function

The cosine (designated cos) is a trigonometric function. In a right triangle, the cosine of an angle is the ratio of the adjacent side to the hypotenuse (the longest side). For example cos(45) = 0.71. The cosine ranges between -1 and 1. The inverse cosine function, sometimes designated arccos(x) and sometimes cos^-1(x), is the function that reverses the cosine. For example, arccos(0.71) = 45. The inverse cosine is defined for x between -1 and 1.

Things You'll Need

Scientific calculator

Instructions

- 1
  Pick values between -1 and 1 at which to evaluate the inverse cosine. For example, you could pick -1, -0.5, 0, 0.5 and 1. The exact values do not matter, but you should pick about five points.
- 2
  Evaluate the inverse cosine at those points. You can do this on a scientific calculator, the inverse cosine key may be labeled "acos," "cos^-1" or "arccos." For example, arccos(-1) = 180, arccos(-.5) = 120, arccos(0) = 1, arccos (.5) = 60 and arccos(1) = 0.
- 3
  Make tick marks on the x-axis (the horizontal one) at equally spaced intervals between -1 and 1. These need not match the points chosen in Step 1, but in the example, they do match.
- 4
  Make tick marks on the y-axis (the vertical one) at equally spaced intervals between 0 and 180 degrees.
- 5
  Plot the points on your graph, using the tick marks from Steps 3 and 4 as a guide.
- 6
  Connect the points with a smooth curve.

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