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How to Graph Arccos Problems

Arccosine, or inverse cosine, is the pseudo-inverse operation of the trigonometric cosine function. It effectively "undoes" the cosine operation; however, the domain and range of arccosine consist of a subset of values of the original cosine value, so it is not a true inverse function. The domain of arccosine is equal to the range of its cosine counterpart. Similarly, the range of arccosine is equal to the domain of its cosine counterpart. Graphing an arccosine problem is a matter of substituting valid x-values into the function to determine the function's y-value at that point. Then you would plot several of these points on a coordinate plane.

Things You'll Need

Scientific calculator
Graph paper

Instructions

- 1
  Choose the domain of the portion of the arccos graph that you want to plot. For example, (-1, 1), one complete period of the arccos function.
- 2
  Substitute multiple values within the chosen domain into the arccos(x) problem. For example, to graph the equation f(x) = arccos(x), with a domain of (-1, 1), substitute multiple values within the domain. These can include arccos(-1) = π, arccos(-0.5) = 2.1, arccos(0) = 1.57, arccos(0.5) = 1.05 and arccos(1) = 0.
- 3
  Plot these points onto a Cartesian coordinate plane that is appropriately scaled for the arccos function. For example, the x-axis can have a range of (-π/2, π/2) and the y-axis can have a range of (0, 3), for arccos with domain (-1,1).
- 4
  Draw a smooth curve connecting the points together to form a wave-like shape. You may check the arccos graph for accuracy on a graphing calculator, if you choose to do so.

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