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Polar equations

Polar equations. Polar equations take on one of the following forms: r = some constant or function of θ r 2 = some constant or function of θ θ = some constant. For example:. Graphing on TI Graphing calculator. You can graph the equations that look like

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Polar equations

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  1. Polar equations Polar equations take on one of the following forms: r = some constant or function of θ r2 = some constant or function of θ θ= some constant

  2. For example:

  3. Graphing on TI Graphing calculator • You can graph the equations that look like You have to put the calculator in polar mode. Then you can go to y = and type in the equation. You will notice that when you hit the variable key it types in a instead of an x.

  4. Converting from rectangular equations to polar equations • When converting from rectangular to polar equations you will just replace the x’s, y’s and x2 + y2 with their unit circle relationships. • Remember:

  5. Then you need to use your algebra skills to get the equation in one of the three acceptable forms of a polar equation:

  6. Example 1 • Convert

  7. Example 2: • Convert

  8. Example 3:

  9. Now check • Graph the polar equations from the previous 3 examples and see if they are what you expected. (Stop for a few minutes to give the students time to graph) • Example 1 is a line with a negative slope and a positive y intercept • Example 2 is a circle with a radius of 2 • Example 3 is a parabola that faces up and has a vertex at the origin.

  10. Converting from Polar to rectangular is a bit more difficult • You need to replace every rcosθ with x, replace every rsinθ with y, and replace every x2+y2 with r2 Then use your algebra skills to solve the equation for r or r2

  11. Tips and techniques • Sometimes you need to cross multiply to get the r and the sinθ or the cosθ together. • Sometimes you have to multiply both sides of the equation by r to get an rcosθ or an rsinθ • Sometimes you have tosquare both sides of the equation to get an r2

  12. Example 4

  13. Example 5 :

  14. For the last example, use your algebra skills to figure out what type of conic section the equation makes. Put the equation in standard rectangular form. • Now

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