Amplitude, period and phase shift
Real waves swing by different amounts, repeat at different rates, start at different times and balance at different levels. Where does each of those live in the formula?
Where you are 4 inside
What this area is about
The graphs of y = \sin x and y = \cos x swing between -1 and 1, balance on the x-axis and repeat every 2\pi (with x in radians). A general sinusoid y = a\sin\big(b(x - h)\big) + k, with a \ne 0 and b \ne 0, changes each of those, one number at a time, and every number can be read off the formula.
How these fit together
Two definitions on the output. Amplitude and reflection: the amplitude is |a|, and a < 0 flips the wave over its midline. Midline and vertical shift: adding k moves the wave so it balances on y = k, without changing the amplitude.
Two procedures on the input. Finding the period: multiplying the input by b gives period \displaystyle \frac{2\pi}{|b|}. Phase shift: the sideways slide h can only be read once the input is factored as b(x - h), so in \displaystyle \sin\left(3x - \frac{\pi}{2}\right) it is \displaystyle \frac{\pi}{6}, not \displaystyle \frac{\pi}{2}.
A path through it
Amplitude comes before the midline lesson, which uses it. The period comes before the phase shift, which first squeezes the wave by b.
With all four, you can write an equation from a wave and combine a sine and a cosine into one wave.