Question

What is the period of `f(t)=sin( ( 5 t) /4 )`?

Answer 1

`f(t)=sin((5t)/4)` has a period of `(8pi)/5`

Explanation:

`sin(theta)` has a period (i.e. a pattern that repeats every increment) of `2pi`

For `sin(theta/2)`, `theta` would need double the incremental distance to reach the repetition point.
i.e. `sin(theta/2)` would have a period of `2xx2pi`

and
`sin(theta/4)` would have a period of `4xx2pi = 8pi`

Similarly we can see that
`sin(5*theta)` would have a period of `(2pi)/5`

Combining these two observations (and replacing `theta` with `t`)
we have
`color(white)("XXX")sin((5t)/4)` has a period of `2pi*4/5 = (8pi)/5`