Polar Bear Math
 

Plotting Functions on Polar Graphs

Just like you can plot functions on regular graph paper, you can plot functions on polar graph paper. The function \(y = Ax\) is a straight line on rectangular graph paper; \(r = A\theta\) is a spiral on polar graph paper. There is no reason we need to limit \(\theta\) to the range [0, 360]; angles go on forever, they just keep going around the polar plot. They can also be negative. Unless otherwise specified, \(0 \le \theta \le 360^\circ\).

\(r=\theta/360\)
\(0\le\theta\le 1800^\circ\)
plot of spiral function
\(r=1+sin\:\theta\)  

plot of cardioid function

 

\(r=2.5+(sin\:40\theta)(1-cos\:3\theta)\) plot of "flower" function

You can get some amazingly pretty results when you experiment with sin and cos functions!

 
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Polar Plotting with TI-83/84 Calculators
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