What kind of graph is the graph of the polar equation r = ΘsinΘ? How does it look like?

Question

What kind of graph is the graph of the polar equation r = ΘsinΘ? How does it look like?
Θ = theta
^_^

Answer 1

It's a series of increasingly larger loops, depending on how large you allow theta to grow before you stop plotting points. (There is one loop for each pi radians.)

Each loop more or less "sits" on top of the origin. The initial loop is very lopsided to the left. Each successive loop is larger and less lopsided. Ultimately, the loops would essentially be very large circles sitting on the origin.

Answer 2

Hi Kevin, It looks like two loops, the smaller inside the bigger. If you go to
http://www.scilab.org/download/index_download.php?page=release.html

you should be able to download a free software that will let you plot theta against theta*sin(theta) yourself , then you can see exaclty what it looks like. Alternatively if you have a spreadsheet program which offers the possibility of displaying x,y plots you can set up something similar. I must admit that I really like graphs - they're so good for speeding up problem solving in many situations , even if it is just for determining initial guesses for some iterative solution.

Best of Luck - Mike

Answer 3

for Θ =0, Θ = pi
r=0
and dr/dΘ = sin Θ + Θ cos Θ
Now get the maximums and minimums and sketch it lightly.

or else convert to Cartesian...

It's a double loop above the initial line if you must know.

Answer 4

--> sinx - cosx = 2 --> sinx - sin(pi/2 - x) = 2 --> 2*sin((x - (pi/2 - x)) / 2) * cos((x + (pi/2 - x)) / 2) = 2 --> sin((2x - pi/2) / 2) * cos(pi/4) = a million -->sin((2x - pi/2) / 2) * a million/sqrt(2) = a million --> sin(x - pi/4) = sqrt(2) --> (x - pi/4) = arcsin(sqrt(2)) --> x = arcsin(sqrt(2)) + pi/4 ---------now now no longer accessible

Answer 5

take, dr=dQdsinQ
=QcosQ
thats a circle