Graphing Polar Equations in Desmos
1.  Go to desmos.com

2.  Click the big red button to launch the calculator.

3.  Change the setting by clicking on the wrench in the upper right hand corner. See Image 1

4.  Choose "Polar"  See Image 2

5.  Your new graphing canvas should look like image 3.


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Image 1
Image 2
Image 3
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Graph each of the following:  r=2, r=3, r=4.  What types of graphs are formed?  What happens as "r" gets larger?
Instead of graphing r= a single number, let's change the number to a slider "a" .  Graph r=a and move the slider "a" back and forth.  Describe the graph as the slider changes.
Now let's graph some roses.  Graphs of the type r=acos(n*Theta) and r=asin(n*Theta) will generate a rose looking graph.  Let's graph r=3sin2Theta.  Hint-Type "theta" in desmose and it will automatically change it to the greek letter for you.  Did you get a cool looking rose?
Play with the number in front of "sin" to see what happens.  How does this change the graph?
Graph things like:  r=2sin2theta and r=4sin2theta
Now that we know what happens when the coefficient in front of "sin" changes, lets explore what happens when we change the number in front of theta.  How does this change the graph?
Graph things like r=2sin3theta and r=2sin5theta
Rose graphing is pretty cool.  Let's make the ultimate rose graph by creating sliders "a" and "b" for the equation r=asinbtheta.  Please copy an image of one of your coolest roses generated by moving the sliders.  Are you having fun yet?
Limacon (pronounced lee-ma-shan ) graphs are also amazing.  These graphs are of the form r=a+bsin theta or r=a+bcos theta .   Let's graph r=0.1+2costheta.  Try to describe the new graph.
Let's not fool around!  Graph r=a+bcostheta where "a" and "b" are sliders.  What happens when you change a?
How about "b"?
Let's graph the "Spiral of Archimedes"  r=theta.  What changes happen to the spiral if you add a coefficient?
Please use your new knowledge of polar graphing to create a most beautiful piece of mathematical art work.  Post your pictures of your original rose and your latest piece of mathematical art to your blog.  Please write a blog post about  how you created each of your pictures using polar graphing techniques and desmos.com.  Please include a link to your latest blog post in the answer space below.  Your blog posts will be shared over twitter, so please make them "Senior" level work.
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