Question

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

1. r = 4 - 4 cos θ
2. r = 4 cos 5θ

Answer 1

need help?

Answer 2

In #1: copy down r = 4 - 4 cos θ. Next, replace that θ by (-θ), and simplify. Is the 2nd equation the same as before, or different from what it was before? What does this result tell you about the symmetry of the graph?

Answer 3

Also more help 1. In the equation r = 4, θ is free. The graph of this equation is, therefore, ... 2. ) for various values of r shows us that we are tracing out the y-axis. ... We graph one cycle of r = 6 cos(θ) on the θr-plane3 and use ... x-axis and gradually pulls in towards the origin as it moves towards the ...... indeed symmetric about the x-axis.

Answer 4

1. x-axis only

Answer 5

2. origin only?

Answer 6

@mathmale @TICOxTICO

Answer 7

yes you are very welcome of our thesis's are they correct?

Answer 8

I believe so. If I got the right answer.

Answer 9

double check on the wiki or other recourse of info. ^-^

Answer 10

by the way
I want to give you something.

Answer 11

what?

Answer 12

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Answer 13

that

Answer 14

lol nice.

Answer 15

your welcome

Answer 16

the epic face

Answer 17

@mathmale Does this look correct?

Answer 18

Take a look at this graph produced by wolframalpha.com for Part #2:

http://www.wolframalpha.com/input/?i=r+%3D+4+cos+5%CE%B8

Do you see any symmetry here? If so, what kind?

You might want to experiment with wolframalpha.com, graphing r=4 cos theta, 4 cos 2 theta, 4 cos 4theta, 4 cos 5 theta, and so on. Use the results to check your answer for Part #2.

Answer 19

It's the first graph I'm looking at right?