The problem with this video is that it explains half of the information really well, but as many have commented it fails to get the correct answers! For symmetry across the x-axis you chose (r, -theta), but it is possible to find the same point with (-r, pi-theta) - so you have to check this too! Similarly, for symmetry across the y-axis you chose (-r, -theta) but (r, pi - theta) must also be checked! I hope this helps :)
@@MatchPointTennis Yes - the sad thing about these tests is that when they work, they work - but when they don't, you actually have no information! I am beginning to think that teaching this topic does more harm than good! :)
Hi, thank you for your explanation. That's what I did too. But the book answer from Ron Larson's Precalculus 3rd edition 10.8 #39 r=5sin(2theta) and the graph shows it's symmetric to all 3 of them. Could you help explain? Thank you!
Pretty sure theyre talking about 4sin2theta. I graphed it on desmos and it does look symmetrical so its throwing me off as well. here's a link to the graph www.desmos.com/calculator/dknclwysqt
Might not necessarily be a mistake but more so that the application of the symmetry test is not perfect. courses.lumenlearning.com/precalctwo/chapter/testing-polar-equations-for-symmetry/ "Passing one or more of the symmetry tests verifies that symmetry will be exhibited in a graph. However, failing the symmetry tests does not necessarily indicate that a graph will not be symmetric about the line π/2, the polar axis, or the pole. In these instances, we can confirm that symmetry exists by plotting reflecting points across the apparent axis of symmetry or the pole. Testing for symmetry is a technique that simplifies the graphing of polar equations, but its application is not perfect."
dude this is a perfectly explained video I owe you my life
Great explanation. Thank you.
Glad it helped!
The problem with this video is that it explains half of the information really well, but as many have commented it fails to get the correct answers!
For symmetry across the x-axis you chose (r, -theta), but it is possible to find the same point with (-r, pi-theta) - so you have to check this too!
Similarly, for symmetry across the y-axis you chose (-r, -theta) but (r, pi - theta) must also be checked!
I hope this helps :)
Thank you for the comment
In this case, you would get the same thing. For example about the x-axis, you can replace (r,theta) with (r,-theta), or (-r,pi-theta)
@@MatchPointTennis Yes - the sad thing about these tests is that when they work, they work - but when they don't, you actually have no information! I am beginning to think that teaching this topic does more harm than good! :)
Probably the best math video explanation I have seen in my life, thanks so much!!
Hi, thank you for your explanation. That's what I did too. But the book answer from Ron Larson's Precalculus 3rd edition 10.8 #39 r=5sin(2theta) and the graph shows it's symmetric to all 3 of them. Could you help explain? Thank you!
Thank you so much Nicholas
If you look at the graph of the function, it actually does have symmetry around the pole and the polar axis...
which example?
Pretty sure theyre talking about 4sin2theta. I graphed it on desmos and it does look symmetrical so its throwing me off as well. here's a link to the graph www.desmos.com/calculator/dknclwysqt
I will check to make sure I did not make a mistake. Thank you for showing me
Might not necessarily be a mistake but more so that the application of the symmetry test is not perfect. courses.lumenlearning.com/precalctwo/chapter/testing-polar-equations-for-symmetry/
"Passing one or more of the symmetry tests verifies that symmetry will be exhibited in a graph. However, failing the symmetry tests does not necessarily indicate that a graph will not be symmetric about the line π/2, the polar axis, or the pole. In these instances, we can confirm that symmetry exists by plotting reflecting points across the apparent axis of symmetry or the pole. Testing for symmetry is a technique that simplifies the graphing of polar equations, but its application is not perfect."
Thank you very much for this comment, was trying to figure out wtheck was happening.
so isn't this like if-then logic, not iff logic, so if the test doesn't work out, there still may be symmetry and you just get no conclusion?
the graph is symmetric about polar axis,theta=90 and also origin
Thanks جزاك الله خيرا ❤
this helps a lot. my professor is so bad at explaining
r=(theta)sin(theta) does not show symmetry
but replacing theta with -theta gives r.
plz explain this
Thanks for keeping it simple
Glad It was helpful!
Odd, according to my book it fulfills all three of the tests
You are probably correct then, but I think I was only testing one specific test, not seeing whether it was all three. Thank you for the comment
By definition it fails to have polar axis. See above work part
1
You should not read such book😂😂😂
It does
Actually all three symmetries can be verified IF you remember the equation sin(2a) = 2sin(a)*cos(a)
y?
Thank you so much. Help me a lots😁
Im so lost, my teacher told us that they wouldn’t pass the pole unless they were r^2, is that true?
not sure
thank you sir.
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This was very helpful , thank. I am subscribing!
THANK YOU SO MUCH
This was helpful, thanks.
My pleasure
Thanks a lot, I appreciate it.
Awesome video thx
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Thank u .
thank u sir
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Anytime