Question 1114138
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sec(x) is the reciprocal of cos(x); its period is the same as cos(x), which is 2pi.<br>
The "3" in 3sec(x/2) does not affect the period.  The period is the range of values of x for which x/2 goes from 0 to 2pi:<br>
{{{0<=(x/2)<2pi}}} -->  {{{0<=x<4pi}}}<br>
So the period of 3sec(x/2) is 4pi.<br>
A shortcut for finding the period of sec(ax) (or sin(ax), or cos(ax), or csc(ax)) is
{{{period = 2pi/a}}}<br>
But I think it is more instructional to understand WHY that shortcut works:<br>
{{{0<=ax<2pi}}}  -->  {{{0<=x<2pi/a}}}