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How to Graph Secant and Cosecant Functions

The trigonometric functions are useful for more than surveying. They're often used to model periodic phenomena, i.e., phenomena that are repeating. Most people are familiar with the basic sine, cosine and tangent functions. The secant and cosecant functions are less rarely encountered, but are also useful for modeling types of phenomena.

Calculator with trigonometric functions
Graph paper

Instructions

- 1
  Set your calculator in radians. Take the cosine of the numbers -pi, -pi/2, -pi/4, 0, pi/4, pi/2 and pi.
- 2
  Take the reciprocal of the cosine of each of the numbers. These points plus the original points form coordinate pairs.
- 3
  Plot the coordinate pairs on graph paper and connect the points with a smooth curve. This produces the graph of the secant function. To produce the graph of the cosecant function, redo this procedure using sine instead of cosine.

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