Ask your own question, for FREE!
Mathematics 11 Online
InsatiableSuffering:

So I have some polar symmetry questions.

InsatiableSuffering:

\[3. r=4\cos(2\theta)+1\] \[Pole symmetry: -r=4\cos(2\theta)+1\] \[\pi/2 symmetry: -r=4\cos(-2\theta)+1 \to -r=4\cos(2\theta)+1\] How is this polar equation symmetrical over pi/2 and the pole

InsatiableSuffering:

\[4.r ^{2}=9\sin(2\theta)\] \[r=\sqrt{9\sin2\theta}\] What is the correct way to prove symmetry for this equation? I found that there's no symmetry over pi/2 and the polar axis, but I found there to be symmetry over the pole. That happens to be wrong as well, so can somebody show what steps should be taken?

InsatiableSuffering:

\[6.r=1+2\sin(\theta/2)\] \[Polar symmetry:r=1+2\sin(-\theta/2)\] Can somebody prove how this equation is symmetrical over the polar axis?

imqwerty:

3. has polar axis symmetry it doesn't have symmetry about the line \(\theta = \pi/2\) or about the pole

InsatiableSuffering:

It doesn't? I plugged in those exact equations on desmos, but they happen to overlap each other perfectly.

imqwerty:

true I think I'm missing something I just replaced r with -r and theta with -theta to check for symmetry about pi/2

InsatiableSuffering:

I'm not sure what's going on either, but when I divided -1 on both sides of the equations I plugged into desmos, I ended up getting a different graph

imqwerty:

oh, I forgot to check for the case when you replace \((r, \theta)\) with \((r, \pi-\theta)\) to check for symmetry about the line \(\pi/2\)

imqwerty:

|dw:1582481689132:dw|

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
Countless7Echos: Ah trying out the whole T.V girl drawing :p (I love drawing eyes)
1 hour ago 8 Replies 5 Medals
kaelynw: starting to draw a hand
2 days ago 16 Replies 2 Medals
Twaylor: Rate it :D (Took 2 days)
2 days ago 7 Replies 0 Medals
XShawtyX: Art, Short Writing Assignment: Imagining Landscapes
4 hours ago 7 Replies 1 Medal
XShawtyX: Chemistry, Help ud83dude4fud83cudffe
3 days ago 13 Replies 1 Medal
kaelynw: tried a lil smt, the arm is off but i like the other stuff
3 days ago 27 Replies 3 Medals
kaelynw: art igg
3 days ago 14 Replies 1 Medal
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!