Question

Pre calc help? I have no idea how to go about solving this problem, so help is appreciated. If you could show me step by step how to this, that'd be great because I have about 20 more to do like this...

4. Identify, graph, and state the symmetries for each polar equation. Write the scale that you are using for the polar axis.
a. r = 1 – 2cosθ
b. r2 = cos(2θ)

Answer 1

Also, the graph I'm supposed to use looks like this..

Answer 2

First you check the symmetry of the polar function given

Answer 3

I note that the cosine function is an even function. If theta is the independent variable, what does the cosine's being an even function tell you ab out the symmetry of the given function?

Answer 4

Errr... That the symmetry of the given function will be even?

Answer 5

put \[(r,-\theta)\] in first equation will give the same function so it is symmetric about X-asis

Answer 6

Then chose the values for theta as \[0 , \frac{ \pi }{6},\frac{ \pi }{ 2 },....\] you will get the value of r

Answer 7

r=1-2 cos theta is a bit tricky to graph because r represents radius and we normally think of radius as being zero or positive. You could find the domain on which \[0 \le 1 - 2\cos \theta\] and graph that section of the curve first, figuring out what to do with negative r later.

Answer 8

the you can easily plot the graph

Answer 9

to answer your question, mathisfun: what you need to do is to identify what kind of symmetry your graph will have. For example, will the graph be symmetric with respect to the y axis? the x axis? or some other reference?

Answer 10

So the equation will be symmetric with the x-axis, for the first one? Than @Joseph91 did you see the graph I attached? Where would I put a point on that based on the one you attached?

Answer 11

for different values of theta you will get r. mark r along those lines along those angles.

Answer 12

I agree that the first graph will be symmetrical with respect to the x-axis. This is clearly showin in your illustration.

Answer 13

Oh okay~ And would the second equation be symmetrical with respect to the y-axis?

Answer 14

It is symmetric to X,Y-Axis

Answer 15

Oh okay! That makes sense.

Answer 16

But what about the graph? @Joseph91

Answer 17

Oh, okay. Thanks!