SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 8 cos 3θ

Algebra ->  Trigonometry-basics -> SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 8 cos 3θ      Log On


   

Question 1140689: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 8 cos 3θ
Found 2 solutions by MathLover1, ikleyn:
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+=+8cos+%283theta%29

about the x-axis:
It is not symmetric about the x-axis because cos%283theta%29+%3C%3E+-cos%283theta%29.

about the y-axis:
It highlight%28is%29 symmetric about the y-axis because highlight%28cos%283theta%29=cos%283%28-theta%29%29%29.

about origin:
for r=8cos+%283theta%29+ plug in r=-r
-r=8cos%283theta%29
r=-8cos%283theta%29=>
it is+not symmetric about the origin because cos%283theta%29%3C%3E-cos%283theta%29.


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+8cos+%283x%29%29+

Answer by ikleyn(52815) 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 = 8 cos 3θ
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The answers by tutor  @MathLover1  are   I N C O R R E C T.

What is even worst,  all her argumentation is   W R O N G.


To find the correct answers,  look into the figure of the web-page

https://www.youtube.com/watch?v=BAiTTMDCNhI

where the plot of the function is shown.


The correct answers are: 

    is the graph symmetric about x-axis ?     - YES.


    is the graph symmetric about y-axis ?     - NO.


    is the graph symmetric about the origin ? - NO.