You need to know what
the three terms amplitude, period, and
phase shift mean,
in the context of talking about the generalized sine and cosine curves shown below:
Generalized Sine/Cosine Curves 
As discussed in the prior section, Graphing Generalized Sines and Cosines, each of these curves is the result of starting with either $\,y = \sin x\,$ or $\,y = \cos x\,$, and then applying graphical transformation(s) chosen from: These transformations affect the ‘height’ (amplitude), ’width’ (period), and ‘left/right positioning’ (phase shift) of the resulting curve. The ideas are made precise below. 

$\color{red}{y = a\sin k(x + b)}$  $\color{red}{y = a\cos k(x + b)}$  
$\color{red}{y = a\sin (kx + B)}$  $\color{red}{y = a\cos (kx + B)}$  
In these equations:

As discussed below,
given any generalized sine or cosine curve,
you should be able to
determine its amplitude, period, and phase shift.
Sample question:
State the amplitude, period, and phase shift of $\,y = 5\sin(3x1)\,$.
In the next section, you will write an
equation of a curve with a specified amplitude, period, and phase shift.
Sample question:
Write an equation of a sine curve with amplitude $\,5\,$, period $\,3\,$, and phase shift $\,2\,$.
AMPLITUDE:


PERIOD:


PHASE SHIFT:

The argument is of the form $\,kx + B\,$.
The expression is of the form $\,a\sin(kx+B)\,$. Here, $\,a = 5\,$, $\,k = 3\,$ and $\,B = 1\,$. The amplitude is $\,a = 5 = 5\,$. The period is $\,\displaystyle\frac{2\pi}{k} = \frac{2\pi}{3}\,$. Setting $\,3x1 = 0\,$ gives $\,\displaystyle x = \frac{1}{3}\,$; the phase shift is $\,\displaystyle\frac{1}{3}\,$. Alternatively, the phase shift is: $\,\displaystyle\frac{B}{k} = \frac{(1)}3 = \frac{1}{3}\,$ 
The argument is of the form $\,k(x + b)\,$.
The expression is of the form $\,a\cos k(x + b)\,$. Here, $\,a = 3\,$, $\,k = 2\,$ and $\displaystyle\,b = \frac{\pi}{5}\,$. The amplitude is $\,a = 3 = 3\,$. The period is $\,\displaystyle\frac{2\pi}{k} = \frac{2\pi}{2} = \pi\,$. Setting $\displaystyle\,2(x+\frac{\pi}{5}) = 0\,$ gives $\,\displaystyle x = \frac{\pi}{5}\,$; the phase shift is $\,\displaystyle \frac{\pi}{5}\,$. Alternatively, the phase shift is: $\displaystyle\,b = \frac{\pi}{5}\,$ 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
