Question

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

r = -2 + 3 cos θ

Answer 1

is there an answer choice

Answer 2

@faariat

Answer 3

what do you mean its either symmetric one of those ways

Answer 4

there are rules for symmetry

Answer 5

If replacing (r, theta) by (r, -theta) gives an equivalent equation, the graph is symmetric with respect to the polar axis (the horizontal axis)

Answer 6

replace theta with -theta in the equation
-2 + cos(-theta) = =2 + cos(theta) = r

therefore it is symmetric with respect to polar axis

Answer 7

Symmetry is a helpful tool when graphing in Polar Coordinates.
If replacing (r; ) by (r;􀀀) gives an equivalent equation, the graph is symmetric with respect
to the polar axis (the horizontal axis). For example, if r = cos and we replace by 􀀀, we
get r = cos(􀀀) = cos since cosine is an even function. Since this is what we started with,
we know that the graph is symmetric with respect to the polar axis.
If replacing (r; ) by (r; 􀀀) or (􀀀r;􀀀) gives an equivalent equation, the graph is symmetric
with respect to the line = =2 (the vertical axis). For example, if r = sin , replacing r by
􀀀r and by 􀀀 gives 􀀀r = sin(􀀀) = 􀀀sin . After we cancel out the negative signs, this
is exactly what we started with, so we know that the graph of r = sin is symmetric with
respect to the line = =2.
If replacing (r; ) by (r; + ) or (􀀀r; ) gives an equivalent equation, the graph is symmetric
with respect to the pole (origin). For example, r = 5 and = =4 satisfy this criterion.

Answer 8

not sure what happened there