http://www.ck12.org Chapter 10. Polar and Parametric Equations
When you go to the window setting you should notice that in addition toXmin,Xmaxthere are new settings called
θmin,θmaxandθste p.
Ifθminandθmaxdo not span an entire period, you may end up missing part of your polar graph.
Theθste pcontrols how accurate the graph should be. If you putθste pat a low number like 0.1 the graph will plot
extremely slowly because the calculator is doing 3600 cosine calculations. On the other hand ifθste p=30 then the
calculator will do fewer calculations producing a rough circle, but probably not accurate enough for your purposes.
Vocabulary
Aparameteris a constant in a general equation that takes on a specific value in a specific equation. In this concept,
the parameters aree,k,β,d. The variablesx,y,r,θare not parameters.
Thepoleis how the origin is described in polar form.
Eccentricityis a parameter associated with conic sections. It is defined by the formulase=caor more generally,
e=PFPD.
Guided Practice
- Convert the following conic from polar form to rectangular form.
r= 2 −cos^3 θ - Graph the following conic.
r= 2 −cos(^3 θ− 30 ◦) - Translate the following conic to polar form.
(x− 3 )^2 +(y+ 4 )^2 = 25
Answers: - There are many ways to convert from polar form to rectangular form. You should become comfortable with the
algebra.