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How to Calculate Polar Graphs

A polar graph is a two-dimensional coordinate system whose points are defined by the equation R = f(θ), where R is the radial length from the vertex of the graph to point and θ is the angle between the horizontal axis and the point. The shape of the polar coordinate system is circular so polar points are more easily represented with circular measurements. Calculating polar graphs require the plotting of multiple points on the coordinate plane in order to determine the shape of the graph.

Instructions

- 1
  Create a T-chart with values for "t" on the left and values for "R" on the right.
- 2
  Use the special radian angles of the unit circle to create values for "t." Since the radian measure of the circumference of a circle equals 2Pi, the values for "t" should be: 0, Pi/6, Pi/4, Pi/3, Pi/2, 2Pi/3, 3Pi/4, 5Pi/6, Pi, 7Pi/6, 5Pi/4, 4Pi/3, 3Pi/2, 5Pi/3, 7Pi/4, 11Pi/6. This is the period from 0 to 2Pi.
- 3
  Substitute each "t" value into the polar function "R" and record the answer on the R-side of the T-chart. For example, for the polar equation R = 4cos2t the values become: R = 4cos(2 * 0) = 4, R = 4cos(2 * Pi/6) = 2, R = 4cos(2 * Pi/4) = 0, etc. Continue this process until you run through the list of "t" values.
- 4
  Plot the points on a polar coordinate graph.
- 5
  Draw a smooth curve connecting the points on the graph, being careful to connect each point to its correct subsequent point. Use the flow of the T-chart to guide you from point to point.

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