MHB Sketch the sinusoidal graphs that satisfy the properties

[eleventhxhour]

12a) Sketch the sinusoidal graphs that satisfy the properties below:
Period: 4
Amplitude: 3
Equation of the Axis: y = 5
Number of Cycles: 2

So, I know how to graph sinusoidal functions, but I can't figure out the max and min that would satisfy both the equation of the axis and the amplitude listed.

 

[MarkFL]

Let's start with the angular velocity $\omega$. For a sinusoid of the form:

$$f(x)=\sin(\omega x)$$

The period is:

$$T=\frac{2\pi}{\omega}$$

This comes from:

$$f(x)=\sin(\omega x)=\sin(\omega x+2\pi)=\sin\left(\omega\left(x+\frac{2\pi}{\omega}\right)\right)=f\left(x+\frac{2\pi}{\omega}\right)=f(x+T)$$

So, letting $T=4$, what must $\omega$ be?