What is the period of #f(t)=sin( ( 5 t ) /3 ) #?

1 Answer
Miguel F.
Dec 31, 2015

In order to find the period of a trigonometric function, we must equal its argument to #0# and #2 pi#, which are the values of the argument which constute a period.

Explanation:

Every trigonometric function, as a sine or a cosine, has a period, which is the distance between two consecutive values of #t#.

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For sine and cosine, period equals #2pi#.

To find the period of a trigonometric function, we must make its argument equal to a period extremes. For example, #0# and #2 pi#.

  • #{5t}/3 = 0 rightarrow t_1 = 0#
  • #{5t}/3 = 2 pi rightarrow t_2 = 6/5 pi#

So period is #Delta t = t_2 - t_1 = 6/5 pi#.

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