list the period, amplitude, interval, and phase shift of: g(t)=5/2sint-pi

i know the amplitude is 5/2 but everything else im not getting.

the regular formula for these is
y=Asin(Bx+C)+D

A is the amplitude
B is the period which you use (2pi/b) to solve.
C is just a constant i assume.
D is the vertical shift.
If theres a neg. A then its a face shift; and the formula changes. but i don't think this is a case for that.

Please help. Thank you.

To find the period, amplitude, interval, and phase shift of the function g(t) = (5/2)sin(t - π), you can use the standard form of the sine function equation, which you mentioned:

y = A * sin(Bx + C) + D

Comparing this equation to the given function, g(t) = (5/2)sin(t - π), we can see:

A = 5/2 (amplitude)
B = 1 (period)
C = -π (phase shift)
D = 0 (vertical shift)

The amplitude, as you correctly mentioned, is 5/2 since the A value represents the coefficient of the sine function, which determines the maximum value the function reaches.

To find the period, we need to use the B value. The period is defined as 2π divided by the absolute value of B. In this case, B = 1, so the period is 2π/1, which simplifies to just 2π.

The phase shift is determined by the C value. In this case, C = -π, so we know that the graph of the function is shifted to the right by π units. The negative sign indicates a rightward shift, as you mentioned.

Finally, the vertical shift is represented by the D value. In this case, D = 0, which means there is no vertical shift. The graph of the function passes through the origin.

To summarize:
- Amplitude: 5/2
- Period: 2π
- Phase Shift: π (to the right)
- Vertical Shift: 0 (no shift)