Please help me with this

Question

Compute the amplitude, midline, and period of the functions.

f(t)= -5sin(pi t) +3

Answer 1

To solve your problem you need to know the basic relations for the sin/cos functions. What I mean is this:

1. For f(t) = A sin(B(t+C)) + D, the values A,B,C,D all do something to the basic function.
2. |A| = Amplitude
3. The Period is 2π/B
4. C = the Phase Shift (left or right movement opposite the sign of C)
5. D = The Vertical shift (the line y = D is called the midline)
6. The function you provided is: f(t) = -5sin(πt) + 3
7. So, we have:
8. |A| = |-5| = 5 = the Amplitude
9. B = π, so the Period = 2π/B = 2π/π = 2
10. C = 0, so there is no Phase Shift
11. D = 3, so the graph is shifted three units upward of the normal sin(t) function, the midline then is the line y = 3

There you have it. Amplitude = 5, Period = 2, Midline is y = 3.

Hope this was helpful for this problem and for others like it.

Good luck, please leave a comment if it was helpful or if it wasn't.

David

Answer 2

f(t)= -5sin(pi t) +3

Amplitude = 5

Midline Value = (-5+3)/2 = (5+3)/2 = -1 +4 = 3

wt = pi t

w= pi

2pi/T pi

T = 2 = time period

Answer 3

f(t) = -5sin(πt) + 3

Amplitude = l -5 l = 5

Period = 2π / (coefficient of t) = 2π / π = 2

The midline of y = -5sin(πt) is the x-axis. Adding 3 to -5sin(πt) shifts the graph of y = -5sin(πt) three units upward. So, the midline for the graph of f(t) - -5sin(πt) + 3 is the line y = 3.