Values of b giving a set number of zeros of sin bx

The constant \(b\) is positive.

1. Show that the solutions of \(\sin bx=0\) with \(x\ge0\) are \(x=\dfrac{k\pi}{b}\), where \(k=0,1,2,\ldots\)[2]
2. Find the number of solutions of \(\sin bx=0\) in \(0\le x\le2\pi\) when \(b=2.5\).[2]
3. Find the set of values of \(b\) for which \(\sin bx=0\) has exactly \(7\) solutions in \(0\le x\le2\pi\).[3]