1. The problem statement, all variables and given/known data
I'm writing a lab report on drag on a non-rotating cylinder. The drag coefficient is calculated using the Pressure co-efficient. The problem I'm facing is that my lab states that the pressure on the cylinder can be predicted by [tex]\left(p-p_{0}\right)_{max} \times cos(\theta) [/tex]

3. The attempt at a solution
The research I've done on the subject leads me to conclude that the pressure on a cylinder can be predicted by [tex]\left(p-p_{0}\right)_{max} \times \left(1-4sin^{2}(\theta)[/tex] instead of the above mentioned equation.

The following is a plot I did in pylab with the experimental plot in blue and the therotical plot in green (using the 2nd equation). The y-axis represents the coeffiecent of pressure while the x-axis is the position from the stagnation point on the cylinder, in degrees.

My question is, am I missing something? Or is my lab wrong on this? I've been literally reading every material I can get my hands on for the past 3 or 4 hours and I'm still terribly confused.

EDIT: The following is the text from my lab notebook which confuses me.

If I substitute [tex] v = 2U\sin\theta[/tex] in the above equation and cancel various terms, I end up with the following:

[tex]C_{p} = 1 - 4\sin^{2}\theta[/tex]

Does this make sense? I have not studied this material into this much depth, I knew Bernoulli but I don't know how we end up with [tex] v = 2U\sin\theta[/tex], so I just took it on faith from the above mentioned website and did the derivation.

I just want to show a theoretical pressure distribution i.e pressure distribution around a cylinder in a ideal flow, thats why I'm hunting for a function (and ended up with the above mentioned one) for Cp in terms of the position of the cylinder.

your equations are correct. It seems to me that if you read the section "Flow Past a Fixed Circular Cylinder" in the link you provided, you will know how v = 2 U sin(theta)