Question

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

r = -5 - 5 cos θ

Origin only

x-axis only

y-axis only

No symmetry

Answer 1

Can you draw it for us? *The picture makes it obvious*

Answer 2

Alright well here's a hint...you have a cos function (an even function)....to test if the graph is symmetric about the x-axis...you replace θ in the equation with -θ and see if the resulting equation is the same

r = -5 - 5 cos θ

after replacing θ with -θ ...

r = -5 - 5 cos(-θ)

Now we know that cos is an even function so that cos(-θ) = cos(θ) so this means that the resulting equation would be

r = -5 - 5 cos θ

just like your original equation...so your graph would be symmetric about the x-axis

Answer 3

Just in case that's confusing....Here's a good rule of thumb to remember about polar functions and symmetry...

A polar curve is symmetric about the x-axis if replacing θ by -θ in its equation produces an equivalent equation, symmetric about the y-axis if replacing θ by pi-θ in its equation produces an equivalent equation, and symmetric about the origin if replacing r by -r in its equation produces an equivalent equation.

Answer 4

thank you @johnweldon1993

Answer 5

No problem!