SOLUTION: Period of 3sec x\2

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Question 1114138: Period of 3sec x\2
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


sec(x) is the reciprocal of cos(x); its period is the same as cos(x), which is 2pi.

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:

0%3C=%28x%2F2%29%3C2pi --> 0%3C=x%3C4pi

So the period of 3sec(x/2) is 4pi.

A shortcut for finding the period of sec(ax) (or sin(ax), or cos(ax), or csc(ax)) is
period+=+2pi%2Fa

But I think it is more instructional to understand WHY that shortcut works:

0%3C=ax%3C2pi --> 0%3C=x%3C2pi%2Fa