



Trig equations look like this:




Y = 2sin(2X) 





Writing this in polar form is easy, 


in fact, it is already in polar form! 


X is the
angle. 


2sin(2X) is
the distance from the origin point. 





The only
change we make in the polar graphing 


is to change the letter Y in
the equation to the Greek letter "r" 





This looks
like the lower case p but is actually the Greek letter rho. 





This love
affair that math types have with Greek letters is AMAZING! 


It's almost
like they want people to say "It's all Greek to me"; and
maybe they do! 





Anyway, a trig
equation in polar form would look like: 





r
= 2sin(2X) 





Don't get all
hung up on the "r"
thing.
It's just another name for Y. 





Now
we plot
some points and graph the equation. 


If the
equation is difficult, 


we can use a partial step or two between the
X and the "r". 





Graphing this
we get: 





X 
sin2X 
2sin2X 

X 
sin2X 
2sin2X 
0 
0.000 
0.000 




10 
0.342 
0.684 

190 
0.342 
0.684 
20 
0.643 
1.286 

200 
0.643 
1.286 
30 
0.866 
1.732 

210 
0.866 
1.732 
40 
0.985 
1.970 

220 
0.985 
1.970 
50 
0.985 
1.970 

230 
0.985 
1.970 
60 
0.866 
1.732 

240 
0.866 
1.732 
70 
0.643 
1.286 

250 
0.643 
1.286 
80 
0.342 
0.684 

260 
0.342 
0.684 
90 
0.000 
0.000 

270 
0.000 
0.000 
100 
0.342 
0.684 

280 
0.342 
0.684 
110 
0.643 
1.286 

290 
0.643 
1.286 
120 
0.866 
1.732 

300 
0.866 
1.732 
130 
0.985 
1.970 

310 
0.985 
1.970 
140 
0.985 
1.970 

320 
0.985 
1.970 
150 
0.866 
1.732 

330 
0.866 
1.732 
160 
0.643 
1.286 

340 
0.643 
1.286 
170 
0.342 
0.684 

350 
0.342 
0.684 
180 
0.000 
0.000 

360 
0.000 
0.000 









How pretty! 


copyright 2008 Bruce Kirkpatrick

