Question 1101965
Here's the plot:
{{{ graph( 400, 400, - (8/5)*pi, (8/5)*pi, -3, 3, 2*cos( 5x ) ) }}}
And here is a plot of {{{ r = 2*cos( theta ) }}} :
{{{ graph( 400,400, -4*pi, 4*pi, -3, 3, 2*cos( x ) ) }}}
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Any cosine function must be symmetrical about the y-axis
and {{{ cos( 5*theta ) }}} is no different
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Start at {{{ 5*theta = 0 }}} and rotate positive:
{{{ 5*theta }}} - - - - - - - - {{{ 2*cos( 5*theta ) }}}
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0 - - - - - - - - - - - - - - 2
pi/2 - - - - - - - - - - - -  0
pi  - - - - - - - - - - - - - -2
3pi/2  - - - - - - - - - - - -  0
2pi  - - - - - - - - - - - - -   2
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And, if you rotate in the negative direction, you get
exactly the same result, so there is symmetry about 
the y-axis