Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 5 cos 5θ

Answer 1

keep in mind cos is an even function (that is cos(-t)=cos(t) )
you have r=5cos(5t)

see if you have (r,-t) on the graph
if you do then it is symmetric about the x-axis



see if you have (-r,-t) on the graph
if you do then it is symmetric about the y-axis




see if you have (-r,t) on the graph
if you do then it is symmetric about the origin

Answer 2

is it symmetric on the y-axis? @freckles

Answer 3

how do you figure that?

Answer 4

idk

Answer 5

here an example:


let's look at r=sin(5t)

sin is an odd function (that is sin(-t)=-sin(t))


so let's check x-axis symmetry?
is (r,-t) on the curve?
r=sin(5*-t)
r=-sin(5t)
as you see the equation r=-sin(5t) is not the same as r=sin(5t)
so no we don't have x-axis symmetry


so let's check y-axis symmetry?
is (-r,-t) on the curve?
-r=sin(5*-t)
-r=-sin(5t)
r=sin(5t) this is the same as what our equation r=sin(5t)
so yes we have y-axis symmetry


so let's check origin symmetry?
is (-r,t) on the curve?
-r=sin(5t)
no r=-sin(5t) is not the same as r=sin(5t)
so no we don't have origin symmetry



all you have to do is use the guideline I gave you above

Answer 6

go through your check list
the first thing on the check list is (r,-t) on the curve? plug in and see if

Answer 7

r = 5 cos 5t


can you plug in (r,-t) into that equation?