Question

Y = 5sin (2x) + 4 What's the amplitude, period, phase shift, and vertical shift?

Answer 1

       Y = 5 sin(2x) + 4

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 .