This is a bit confusing

Question

Find the amplitude, period and phase shift of the function defined by each of the following equations, and sketch the graph of one complete period.

(3.1) y = 4sin 1/2 * (x + pi) (10)

(3.2) y = cos(3x - pi) + 2

Answer 1

General formula is

AsinB(x + C) + D where A = amplitude, 2pi/B = period, -C = phase shift, D = midline

for 3.1 A=4=amplitude, B=1/2, period = 2pi/(1/2) =4pi, C=-pi/2=phase shift, 10 is probably D (unless A=4(10)=40, but that's a very strange way to write the problem)

4sin(1/2)*(x+pi)(10) probably was meant to mean 4sin(x/2+pi/2) +10? but it's ambiguous. It might even have meant 4sin[(5)(x+pi)] if 10 times 1/2 was intended or maybe the (10) refers to the number of a problem? like 3.1, 3.2? half the problem is sometimes figuring out what the problem really is.

3.2 y=cos(3x-pi) +2= cos[3(x-pi/3)] A=1=amplitude, B=3, C=pi/3= phase shift, D=2 period = 2pi/B= 2pi/3

D is useful in sketching the graphs. It's the midline, the value of y which is half way between the max and minimum y values.