Question

Someone PLEASE HELLLLLP!!! NEED HELP!! DESPERATE!

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 2 cos 5θ

Answer 1

the 2 stretches the graph and doesn't affect symmetry. the 5 does the same. all you are concerned with here is the graph of cosine.

Answer 2

You know that cosine of 0 is 1. Cosine if pi/2 is 0. Cosine of -pi/2 is also 0. So this tells you that the graph is symmetric about the y-axis.

Answer 3

See thats what confused me. I graphed it and its symmetrical across x axis.

http://www.wolframalpha.com/input/?i=r+%3D+2+cos+5%CE%B8

Answer 4

Nah, it's only sym about the y-axis. look at the 3rd pic on wolfram, or the pic i uploaded.

think of the y axis as a mirror. you see exactly the same reflection on the left as the right. now think of the x as a mirror. it would be exactly the same, but it's not, so it's not symmetric about x axis

Answer 5

if you folded the graph in half on the y axis, the lines would match exactly. if you fold it about the x, they would not match

Answer 6

Not for the polar graph. In my lesson, we have only used the polar graph and thats what comes up on my calculator.

Answer 7

the regular cosine function is symmetrical about the y axis, but you are using polar coordinates, in which the function you have is symmetrical about the x axis

Answer 8

oh i see

Answer 9

i did not know you were talking about the polar graph. :)

Answer 10

No problem. I have to answer this question through algebraic work proving whether or not its symmetrical

Answer 11

in that case yes, x-axis, not y

Answer 12

convert polar coordinates to euclidean coordinates and prove that x= \y\ (absolute value)

Answer 13

then it is symmetrical about the x axis

Answer 14

that sounds like a great approach @SalvadorV

Answer 15

so far I have proven that x is symmetric; by taking r=2cos5(theta) and changing (r, (Theta)) to (r,-(theta)) but I cant figure out how the algebra for the origin, where the (r,(theta)) is changed to (-r,(theta)) could you help with that?

Answer 16

well what sal was saying is to convert the polcar coordinate (r,theta) to rect by doing some trig. x = rcos(theta), y = rsin(theta)

Answer 17

then show through algebra that \[x = |y|\]

Answer 18

the conversion formulas are
\[x = rcos\theta\\y=rsin\theta\]

Answer 19

my lesson does it keeping polar variables. and my teacher probably wants them that way too.

Answer 20

yup, exactly, what you have to do is just that

Answer 21

here let me type up what I am having trouble with

Answer 22

but pizza is soooo good :3

Answer 23

I think the test for symmetry about the x-axis involves something like:

if the point (r,theta) lies on the graph, then the point (r,-theta), or (-r, pi - theta) lies on the graph

Answer 24

No for this one im doing the origin symmetry

Answer 25

Ive already proven the x and y

Answer 26

so (-r,-theta) and (r, theta+ pi) is the theorem you need

Answer 27

er, test

Answer 28

I would just use that theorem as proof and call it a day. :) But I don't like proofs... If I think of anything I will come back.

Answer 29

(using the theorem to prove by example)

Answer 30

I think it would be best for the origin symmetry to prove wheter or not the radius is the same when you take opposite sides, this case would be tha radius in 0 and 180, in 90 and 270, in 45 and 225, and in 135 and 315. If they are not the same value then it's because it's not symmetrical

Answer 31

^^ that sounds good

Answer 32

I havent worked with polar coordinates that much but I believe that you can use 90 and -90 (-90 being 270), but as I said I'm not sure

Answer 33

the thing is that I believe that to prove that it is symmetrical about x, x and y need to exist, and if we are strict, in polar coordinates they dont. thats why I believe you should convert them to euclidean coordinates