Polar And Parametrics

Front 1

Rectangular formula for circle and ellipse

Back 1

circle: x^2+y^2=1
ellipse: (x/a)^2 + (y/b)^2 = 1

Front 2

Parametric circle
radius=b, centered at (c,d)

Back 2

x=bcost+c
y=bsint+d
rotated counter-clockwise from 0 to 2pi

Front 3

Parametric ellipse
(x/a)^2 + (y/b)^2

Back 3

x=acost
y=bsint

Front 4

dy/dt without eliminating parameter
and d^2y/dx^2

Back 4

(dy/dt)/(dx/dt)
and d/dt(dy/dx)/(dx/dt)

Front 5

Polar to rectangular coordinates

Back 5

x=rcos(theta)
y=rsin(theta)

Front 6

Picture for
r=a(1-cos(theta))

Back 6

Front 7

Picture for
r=a(1+cos(theta))

Back 7

Front 8

Picture for
r=a(1+sin(theta))

Back 8

Front 9

Picture for
r=a(1-sin(theta))

Back 9

Front 10

For limacons with formula r=a+bcos(theta) how will it look? Dimpled or not?

Back 10

Front 11

Picture for r=acosn*(theta)

Back 11

for n=2 to n=6
n petals if n is odd, 2n petals if n is even

Front 12

Picture for r=asinn*(theta)

Back 12

for n=2 to n=6
n petals if n is odd, 2n petals if n is even

Front 13

Picture for r=a(theta)

Back 13

Front 14

Picture for:
r=asin(theta)
r=-asin(theta)
r=acos(theta)
r=-acos(theta)
with a=diameter of circle

Back 14

r=asin(theta) is circle above x-axis
r=-asin(theta) is circle below x-axis
r=acos(theta) is circle right of y-axis
r=-acos(theta) is circle left of y-axis
with a=diameter of circle

Front 15

dy/dx for polar

Back 15

dy/dx= (rcos(theta)+sin(theta)dr/d(theta))/(-rsin(theta)+cos(theta)dr/d(theta))

Front 16

length of polar curve

Back 16

L=integralfromalphatobeta of sqrt(r^2+(dr/d(theta))^2)