Question

I have a question: Is there a method to determine the symmetry of a function ALGEBRAICALLY or not graphically?

Answer 1

For example:
r = 3 cos 5θ

Answer 2

you can check if \(f(\theta)=f(-\theta)\)

Answer 3

I get r= - 3 cos5 θ

Answer 4

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

Answer 5

f(-theta)=f(theta)=> function is symmetric
if,
f(-theta)=-f(theta)=>function is retricemetric

Answer 6

let the function be y=f(x),
replce x by -x in the problem if
f(-x) comes out to be f(x) yes the function is symmetric about y axis otherwise not

Answer 7

To me, to polar equation like that, cos is always symmetric about x-axis, and sin is y-axis.

Answer 8

Oh ok and how do I determine if it is symmetric about the x-axis or origin
?

Answer 9

http://www.most.gov.mm/techuni/media/EM_02011_chap5b.pdf

Answer 10

A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with y.

Answer 11

solvereplacing x and y's both for origin

Answer 12

ohhhhhh ok thanks so much guys♥