Ethen Choy's High School Portfolio

Topics in Calculus Unit 4: Parametric & Polar Equations

Rectangular to Polar form

( tan-1(y/x) , sqrt(x^2 + y^2) )

Polar to Rectangular form

( r*cos(a) , r*sin(a) )

Rose Curves

r = acos(nθ)

If n is odd:

# of petals = n
If A is positive, first petal goes on positive x-axis, and there will be more petals on the positive side (right side) of the y-axis.
If A is negative, first petal goes on negative x-axis, and there will be more petals on the negative side (left side) of the y-axis.

If n is even:

# of petals = 2n
Petals go along all axes.

r = asin(nθ)

If n is odd:

n = # of petals
If A is positive, there will be more petals on the positive side (top side) of the x-axis.
If A is negative, there will be more petals on the negative side (bottom side) of the y-axis.

If n is even:

# of petals = 2n
Petals avoid touching all axes.

Example: r = 3sin(5θ)

Length: 3

Number of petals: 5

How to determine type of limacon

Examples of limacons

Inner Loop

Cardioid

Dimpled

Convex

Lemniscates

The radius will be the length from the origin to the farthest point on each loop.

Lemniscates example

Spiral

a determines the starting point of the spiral.

b determines how wide the spiral goes.

Spiral example

Parametric Equations

Graphing is on top, elimination is on bottom

Projectile Motion

x = vcost +x0

y = -16t^2 + vsint +y0

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