SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 + 3 sin θ choices below y-axis only Origin only x-axis only No symme

Algebra ->  Trigonometry-basics -> SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 + 3 sin θ choices below y-axis only Origin only x-axis only No symme      Log On


   

Question 1138249: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -3 + 3 sin θ
choices below

y-axis only

Origin only

x-axis only

No symmetry
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r+=+-3+%2B+3+sin%28+theta%29
polar plot:
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test:
replace theta with -theta
polar plot: r+=+-3+%2B+3sin%28-theta%29
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=>polar equation is changed; the graph is NOT symmetric about the+x-axis

replace theta with %28pi-theta%29+
r+=+-3+%2B+3+sin%28+pi-theta%29
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and you will see that the graph will not change; the graph IS symmetric about the y-axis