The amplitude of the sin itself is 1 . The amplitude of 5sin is 5 .
Every time the "argument" of the sin increases by 2π another period starts. The first period goes from zero until 2x = 2π . So the length of the period is π .
The phase shift is the value of the angle when x=0. That's zero.
The sin itself wiggles up and down, regularly and symmetrically, above and below the x-axis (y=0). In this equation, the whole thing is shifted up 4 units by that +4 on the end, so it's wiggling up and down above and below the line y=4. The vertical shift is +4 .
If this function were an electrical signal, we would say that its period is π seconds, its frequency is 1/π Hz, and it has an AC amplitude of 5 riding on a DC component of 4 .
