Week 6: Graphs of Polar Equations

This week we looked at the Graphs of Polar Equations. 

The Polar Equations had many different Graphs

There were circles, lines, spirals, more circles, rose curves and even more.

We more or less looked at the equation for them.

For circles at the origin
r=a where a is the radius

For Lines through the origins
θ=a

For Spirals:
r=aθ

For Circles with the center on the axis
r=asinθ This is on the y-axis
r=acosθ this is on the x-axis a=diameter

Then for Rose curves
r=asinnθ
r=acosnθ
a means the length of the petal
an odd n=n=number of petals
an even n=2n= number of petals
a^2 =how long
n=how many

for a Lemniscate:
r^2 =acos2θ
r^2 =asin2θ
the sin graph is on the x=y axis

For Cardiods
r=a±asinθ
r=a±acosθ

For Limacons:
r=a±bsinθ
r=a±bcosθ
a/b < 1 interior loop
1<a/b<2 dimpled
a/b≥ 2 convex











This is what we did and how you use these polar equations

SEE YOU NEXT WEEK!!!