Today in Precalculus

• Go over homework• Connection between polar and

rectangular graphs of trig functions• Notes: More on Graphs of Polar

Equations• Homework

a. y = 4cos(2x) b. y = 2 + 2sin(x)

Range: [-4,4] Range: [0,4]Max. r value:4 Max r value: 4

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.

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.

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.

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.

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.

Rose curvePetal length = 3Petals on all axis, so

cos4 petals so n =2

r = 3cos2θ

Dimpled limaconMajority of graph over

negative x-axis, so negative cos

Max r value = 5 = a+ba – b = 1 (where the

dimple is)b=2a=3r = 3 – 2cosθ

Limacon with inner loopMajority of graph over

negative y-axis, so negative sin

Max r value = 5 = a+ba – b = -1 (where the

loop touches)r = 2 – 3sinθ

Rose curvePetal length = 2One petal on y-axis, so

sinFive petals, n = 55 petals should have

one petal on positive y-axis, so sin negative

r = -2sin5θ

Homework

WorksheetPolar Quiz Monday, April 11