Polar Equations and Graphs. 1. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar.

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Presentation transcript:

Polar Equations and Graphs

1. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

2. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

3. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

4. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

5. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

6. Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation (Similar to p.325 #13-28)

Symmetry Condition Polar axis (x-axis)Replace θ by –θ and you get the same equation Line θ/2 (y-axis)Replace θ by π – θ and you get the same equation Pole (origin)Replace r by –r or θ by θ + π and you get the same equation

Graph Forms Θ = α (Line at angle α) rcosΘ = a (Vertical Line) rsinΘ = a (Horizontal Line)

Graph Forms r = a (a > 0) (Circle) r = +2a cosΘ (a > 0) (Circle) r = +2a sinΘ (a > 0) (Circle)

Graph Forms r = a + a cos θ r = a + a sin θ (a > 0) (Cardiod) r = a + b cos θ r = a + b sin θ (0 < b < a) (Limacon without inner loop) r = a + b cos θ r = a + b sin θ (0 < a < b) (Limacon with inner loop)

Graph Forms r 2 = a 2 cos(2θ) r 2 = a 2 sin(2θ) (a > 0) (Lemniscate) r = a sin(3θ) r = a cos(3θ) (a > 0) (Rose with 3 Petals) r = a sin(2θ) r = a cos(2θ) (a > 0) (Rose with 4 Petals)

7. Identify and graph each polar equation (Similar to p.326 #37-60)

8. Identify and graph each polar equation (Similar to p.326 #37-60)

9. Identify and graph each polar equation (Similar to p.326 #37-60)

10. Identify and graph each polar equation (Similar to p.326 #37-60)