Alg 2/Precalc Honors- Special Polar Graphs

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<p>Convex Limacon</p>

Convex Limacon

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(a/b) ≥ 2

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<p>Cardioid</p>

Cardioid

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(a/b)=1

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23 Terms

1
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<p>Convex Limacon</p>

Convex Limacon

(a/b) ≥ 2

2
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<p>Cardioid</p>

Cardioid

(a/b)=1

3
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<p>Limacon with inner loop</p>

Limacon with inner loop

(a/b)<1

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<p>Dimpled limacon</p>

Dimpled limacon

1 < (a/b) < 2

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How many petals if odd

n

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How many petals if even (n ≥ 2)

2n

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Where is at least one petal when its a cos graph

Pole or θ=0

<p>Pole or θ=0</p>
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Where is the initial petal in a sin graph

θ=pi/2/n

<p>θ=pi/2/n</p>
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<p>r=a cos(θ)</p>

r=a cos(θ)

Circle with axis of sym on pole

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<p>r=a sin(θ)</p>

r=a sin(θ)

Circle with axis of sym on θ=pi/2

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<p>r^2=a^2 sin(2θ)</p>

r^2=a^2 sin(2θ)

Lemniscate with axis of sym from pi/2 by the distance of pi/2/n

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<p>r^2=a^2 cos(2θ)</p>

r^2=a^2 cos(2θ)

Lemniscate with axis of sym on pole

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How can you find the number of degrees between petals on a rose curve

2pi/number of petals

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Ellipse

e (eccentricity) < 1

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Parabola

e (eccentricity) = 1

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Hyperbola

e (eccentricity) > 1

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x^2+y^2

What is r^2 equal to

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rcos(θ)

What is x equal to in polar form

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rsin(θ)

What is y equal to in polar form

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y/x

What is tan(θ) equal to

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=k

How do you find the directix

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Horizontal motion is

x=vtcos(θ)

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Vertical motion is

vtsin(θ)-.5gt^2 +h