10.8 – Graphs of Polar Equations
May 15th, 2011 by corricelli
Hello,
Please use this section of our blog to post questions related to Chapter 10, Section 8.
Here is a very nice (long) pdf that breaks down the crucial concepts here.
This is a tutorial on graphing by hand. http://www.analyzemath.com/polarcoordinates/graphing_polar_equations.html
Happy blogging,
Mrs. Corricelli
Ok, so I found the page, disregard the 10.2 comment. I’ll just copy it onto here…
I am sort of confused on how to use symmetry to help graph polar equations. It says to use substitution to see which symmetry applies. But I tried that in #31 on the homework. Calc Chat says the graph is symmetric with respected to theta = pi/2, but I didn’t get this. I’m not sure if i am doing the arithmetic incorrectly or just not understanding the concept.
Hello Laura,
Do not use the symmetry approach as dictated in the book. Use your knowledge of trigonometric functions as we did in class. Sketch to get a general pattern; look for Special Polar Graphs as specified on p. 787.
As for number 31, r=4(1+sin(theta)) = 4 + 4sin(theta), a limacon with a/b = 1 so it is a cardioid. sin(theta)’s max value will occur when theta = pi/2 (since that will make sin(theta) = 1). Sooo 4 + 4sin(theta)’s max value is also there. Similarly, sin(theta)’s minimum value is -1, when theta = 3pi/2. So that is this equation’s minimum value too. This makes this shape an upside-down heart, symmetric with the “y-axis” (line containing the minimum and maximum). It crosses the x-axis at 4 and -4.
Remember you can use your graphing calculator too. Set the mode to degrees and polar. Zoom standard and zoom square. Trace to see these points. Experiment and have fun! Look for patterns! What if the 4 were negated? What if cosine, instead of sine, were used?
Also check out this link to an applet that allows you to plot polar graphs: http://www.ies.co.jp/math/java/calc/sg_kyok/sg_kyok.html.
Hope this helps,
Mrs. Corricelli
is the homework tonight all of the problems given in class or is it like when we usually have reviews and we select from the chapter review, in this case from those numbers you gave us?