Week 6: Graphs for polar equations

Below are two examples of polar equations created to make an image on a polar graph.

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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!!!

Week 5: Polar Coordinates

We looked the Polar Coordinate System, which we have never really used before. We have always used the rectangular coordinate system but not the polar.

The Polar Coordinate System uses (r, θ)
r is the direction it goes in a circle and if the θ>0 then it is counterclockwise if it is less then 0 then clockwise

TO convert polar to rectangular
you use x=rcosθ and y=rsinθ

To convert rectangular to polar you use r^2 =x^2 + y^2 and tanθ=y/x

above is an example of a polar equation being put on the graph. There also are four ways of naming in polar coordinates. Above are the four examples.

These equations are also used to solve for the other side in rectangular and in polar.

Here is an example.

It is similar to verifying but not at the same time.

This is the polar coordinate system

SEE YOU NEXT WEEK!!!