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

r = -3 - 2 cos θ

I think the answer is :y-axis only

Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = -3 - 2 cos θ

I think the answer is :y-axis only

anonymous · Answer

@ganeshie8 @Hero @iambatman @Callisto

ganeshie8 · Answer

$$r(\theta) = -3-2\cos\theta$$

ganeshie8 · Answer

replace $\theta$ by $-\theta$ : 
$$r(-\theta) = -3-2\cos(-\theta) = -3-2\cos\theta = r(\theta)$$

ganeshie8 · Answer

the graph is not changing when you change $\theta$ by $-\theta$
that means the graph is symmetric about x axis (why ?)

anonymous · Answer

So is that when I graph it It sticks a bit out on the x axis

ganeshie8 · Answer

yes top and bottom looks same when the graph is symmetric about x axis

ganeshie8 · Answer

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anonymous · Answer

oh okay, Thanks so much.

ganeshie8 · Answer

x axis is the line of reflection ^

anonymous · Answer

So it would gBE y axis if it is the same on the y

ganeshie8 · Answer

Exactly! below graph is symmetric about `y` axis :

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ganeshie8 · Answer

i think we can say human body is symmetrc about y axis

ganeshie8 · Answer

ofcourse when you stand straight up..

anonymous · Answer

when would it be neither? when its a line?

ganeshie8 · Answer

depends on the line, can you draw what you have in mind ?

ganeshie8 · Answer

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anonymous · Answer

oh okay cool thanks! I saw a circle like that the other day

ganeshie8 · Answer

i think a circle is symmetric about plenty (infinite) of lines... 
can you guess few of them ?

anonymous · Answer

Of the x and y axis right?

ganeshie8 · Answer

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