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)
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b. y = 2 + 2sin(x)
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Range: [-4,4]
Max. r value:4
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Range: [0,4]
Max r value: 4
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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
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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
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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 – 2 sinθ
r = 1 + 2sinθ
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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
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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.
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Rose curve
Petal length = 3
Petals on all axis, so
cos
4 petals so n =2
r = 3cos2θ
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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
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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
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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
Homework
Worksheet
Polar Quiz Friday, April 11