Question

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

Answer 1

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`.

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`.