Question

Please help! I always give medals and become a fan!
Which features are present in this polar graph? (more than one answer.)
PICTURE ADDED BELOW

a. no symmetry
b. symmetry about the line theta = pi/2
c. symmetry about the pole (0,0)
d. symmetry about the polar axis theta=0.

Answer 1

were you able to get anywhere?

Answer 2

no not really! I'm not really sure how to go about the problem

Answer 3

I'm assuming you've found function inverses before in the past?

Answer 4

uhm it sounds familiar... kind of

Answer 5

actually no that won't work here, nevermind that thought

Answer 6

theta = pi/2 is the angle that's at 90 degrees, so if you were to fold the figure over the y axis, would it match up with itself?

Answer 7

haha okay! (:

Answer 8

no it wouldn't

Answer 9

the y axis is the vertical axis

Answer 10

you sure?

Answer 11

wait so it would then

Answer 12

yes it would, try drawing it out on paper and folding it up yourself

Answer 13

you'll see things match up perfectly (or close enough depending on how accurately it's drawn)

Answer 14

so there is symmetry with respect to the line theta = pi/2

Answer 15

how about with theta = 0?

Answer 16

okay so I know for sure that a. is wrong and b. is right. :)

Answer 17

how would I find that out?

Answer 18

yes a) is out because b) is true

Answer 19

well fold the figure over the x axis and see if things line up

Answer 20

so this would be folding it horizontally, correct? so it wouldn't line up

Answer 21

yep it doesn't line up

Answer 22

so there is no symmetry over the line theta = 0

Answer 23

how about symmetry with respect to the pole (0,0)

Answer 24

how do I do that?

Answer 25

one sec

Answer 26

a polar graph is symmetric with respect to the pole (0,0) if you can rotate the figure 180 degrees and it will line up with itself

Answer 27

so when you rotate the figure 180 degrees, does it line up with itself?

Answer 28

yes

Answer 29

look at the bottom blade

if you rotated it 180 degrees, does that bottom blade line up with either of the top blades?

Answer 30

no

Answer 31

so it's not symmetrical with respect to the pole (0,0)

Answer 32

okay thank you sooooo much!!

Answer 33

you're welcome