Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 5 + 4 cos θ
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@ZeHanz please help
Because of the 5 and 4, you can see that r takes values between 5-4=1 and 5+4=9.
At theta=0 (and theta=2pi), r=9.
At theta=pi (halfway the period), r=.
What does this tell you about possible symmetries?
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@ZeHanz can you finish helping me please?
Well, the graph cannot be symmetrical around the origin, because of this.
Also, because (9,0) and (-1,0) are the points for theta=0 and theta=pi, the y-axis is not an axis of symmetry.
So maybe the only symmetry left is the x-axis.
Because the values of the cosine are the same before and after pi, this is indeed the case.
This is what the graph roughly looks like:
okay? so then how can you tell if it is around the x axis?
Because the points above the x-axis belong to theta between 0 and pi, and the points below to theta between pi and 2pi. The cosine has the same values before and after pi, so the points lie symmetrical with respect to the x-axis.
(Hope you understand what I want to say...)