SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ can you please show all your work and explain or else i won't understand.

Algebra ->  Graphs -> SOLUTION: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ can you please show all your work and explain or else i won't understand.      Log On


   

Question 1101965: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 2 cos 5θ

can you please show all your work and explain or else i won't understand. like in a step by step way
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the plot:

And here is a plot of +r+=+2%2Acos%28+theta+%29+ :
+graph%28+400%2C400%2C+-4%2Api%2C+4%2Api%2C+-3%2C+3%2C+2%2Acos%28+x+%29+%29+
------------------------------------------------
Any cosine function must be symmetrical about the y-axis
and +cos%28+5%2Atheta+%29+ is no different
-----------------------------------
Start at +5%2Atheta+=+0+ and rotate positive:
+5%2Atheta+ - - - - - - - - +2%2Acos%28+5%2Atheta+%29+
----------------------------------------
0 - - - - - - - - - - - - - - 2
pi/2 - - - - - - - - - - - - 0
pi - - - - - - - - - - - - - -2
3pi/2 - - - - - - - - - - - - 0
2pi - - - - - - - - - - - - - 2
-----------------------------
And, if you rotate in the negative direction, you get
exactly the same result, so there is symmetry about
the y-axis