Question

What is the period of the trigonometric function given by `f(x)=2sin(5x)`?

Answer 1

The period is: `T=2/5pi`.

The period of a periodic function is given by the period of the function divided the number the multiplies the `x` variable.

`y=f(kx)rArrT_(fun)=T_(f)/k`

So, for example:

`y=sin3xrArrT_(fun)=T_(sin)/3=(2pi)/3`

`y=cos(x/4)rArrT_(fun)=T_(cos)/(1/4)=(2pi)/(1/4)=8pi`

`y=tan5xrArrT_(fun)=T_(tan)/5=pi/5`.

In our case:

`T_(fun)=T_(sin)/5=(2pi)/5`.

The `2` changes only the amplitude, that, from `[-1,1]`, becomes `[-5,5]`.