Question

Answer check please(:.Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = -3 + 3 sin θ

my answer is origin only?

Answer 1

Hmm that is not quite what I get...remember

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.

If you replace r with -r here...you get

r = 3 - 3sinθ which is not the original equation...it's flipped upside down in this case....

so it is not symmetric about the origin...

try one of the others...

Answer 2

y axis?

Answer 3

That would be correct! You know it isn't the x-axis because when you replace θ with -θ here....you do not get the same equation...because remember sin is not an even function....so yes....it is symmetric about the y-axis

Answer 4

thankyou!(:

Answer 5

No problem! :)