1. Today in Precalculus Go over homework
Connection between polar and rectangular graphs of trig functions
Notes: More on Graphs of Polar Equations
Homework

2. y = 4cos(2x) b. y = 2 + 2sin(x)
Range: [-4,4] Range: [0,4]
Max. r value:4 Max r value: 4

3. Conclusions
Rose curve equations are sin or cos waves in rectangular form with changes only to the amplitude and period. Therefore the range of a rose curve is symmetric to zero.
Limacon curve equations are sin or cos waves in rectangular form with changes to the amplitude and vertical shift. Therefore the range of a limacon curve is not symmetrical to zero.

4. What happens when the “a” is negative in a rose curve?
r = 2 sin3θ r = -2sin3θ
If n is odd, the graph is reflected over the x-axis.
If n is even, the graph doesn’t change. The points plot in a different order.

5. What happens when the “a” is negative in a rose curve?
r = 2 cos3θ r = -2cos3θ
If n is odd, the graph is reflected over the y-axis.
If n is even, the graph doesn’t change. The points plot in a different order.

6. What happens when the “b” is negative in a limacon curve?
r = 1 + 2sinθ r = 1 – 2 sinθ
When b is positive, the majority of the curve is around the positive y-axis
When b is negative, the majority of the curve is around the negative y-axis.

7. What happens when the “b” is negative in a limacon curve?
r = 1 + 2cosθ r = 1 – 2cosθ
When b is positive, the majority of the curve is around the positive x-axis
When b is negative, the majority of the curve is around the negative x-axis.

8. Rose curve
Petal length = 3
Petals on all axis, so cos
4 petals so n =2
r = 3cos2θ

9. Dimpled limacon
Majority of graph over negative x-axis, so negative cos
Max r value = 5 = a+b
a – b = 1 (where the dimple is)
b=2
a=3
r = 3 – 2cosθ

10. Limacon with inner loop
Majority of graph over negative y-axis, so negative sin
Max r value = 5 = a+b
a – b = -1 (where the loop touches)
r = 2 – 3sinθ

11. Rose curve
Petal length = 2
One petal on y-axis, so sin
Five petals, n = 5
5 petals should have one petal on positive y-axis, so sin negative
r = -2sin5θ

12. Homework
Worksheet
Polar Quiz Monday, April 11