What happens when we multiply theta by 2 in sine functions?

The graph of sin theta has an amplitude of 1 and a period of 2pi. That means that one whole revolution occurs from 0 to 2 pi. When you multiply theta by 2, the period is the same, but the graph is shrunk so that 2 revolutions occur from 0 to 2 pi. The amplitude remains unchanged and there is no phase shift. If you multiplied theta by 3, you would have 3 revolutions occur from 0 to 2 pi.