Question 703150
Suppose the problem was {{{ y = cos(x) }}}
As you vary {{{ x }}} from {{{ x = 0 }}} counterclockwise
to {{{ x = 2*pi }}}, and {{{ y }}} varies from 1, 0, -1, 0, 1
At no point is it less than {{{ -1 }}} or greater than {{{ +1 }}}
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Now if the problem is {{{  y = 3*cos(x) }}}, and {{{y}}} varies
from  3, 0, -3, 0, 3
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The period is {{{ 2*pi }}} because I can say
{{{ 3*cos(x)  = 3*cos( x + 2n*pi ) }}} where {{{ n }}} can be 
0, 1, 2 ,3 ...etc.