Question

find the function of the form y=sin bx given the period. Pi over 2

Answer 1

The normal period of \(\sin(x)\) is \(2\pi\).

Answer 2

Now if you need to get to \(x=2\pi\) for the cycle to repeat, then were you to have \(\sin(bx)\) then you need to get to \(bx=2\pi\) for the cycle to repeat. Thus the period is \(2\pi/b\).

Answer 3

So our equation here is \[
\frac{2\pi }{b}=\frac \pi 2
\]

Answer 4

Solve for \(b\) and you're pretty much done.

Answer 5

thanks wio