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How to Graph on a Polar Grid

A polar grid, or polar coordinates, allows you to graph functions such as circles or spirals in a convenient notation. Rather than using a square grid of x and y values as the Cartesian coordinate system does, polar coordinates graph a radius and angle on a grid that resembles a bulls-eye. The radius is called R, and functions are usually written in the form R = ... The angle, t, is measured in radians counter-clockwise from the right-hand half of the horizontal axis.

Instructions

- 1
  Draw a T-chart with the variables t and R at the top.
- 2
  Write several values for t on the chart using radians. A sample list might be 0, pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, and 2pi.
- 3
  Plug the different t values into the equation for the function and write the resulting R values in the R column of the T-chart, using decimal notation.
  
  Example:
  
  R = cos t
  
  For t = pi/3, R = 0.5
- 4
  Graph each line of the T-chart as an ordered pair, first using the R value to go out to the right the distance of the radius on the horizontal axis, then using the t value to rotate counter-clockwise around the circle through the given angle.
- 5
  Connect the dots from the graphed ordered pairs with a smooth curve. Your result is a circle shifted right from the center of the graph until its left edge is on the vertical axis.

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