A sinusoidal function, y = a sinb(x - c) + d has a maximum point at ( pi/4 , 3 )

The period is pi if you take the difference between the max and min and multiple that by 2. Thus b is 0.5.

c is 0 since the max and min and equal distance apart.

I tried plugging pi/4 into your equation and I did not get the same maximum as in the opening post. I believe that b is actually omega (angular speed) rather than the period. If we solve it in this manner, b=2 (when b=2, the period is pi).

I also believe that c is the phase shift rather than the distance of the maximum and minimum. Solving the equation \(3=2\sin\Big(2(\frac{\pi}{4}-c)\Big)+1\) suggests that \(c=\pi*k\), where \(k\in \mathbb{z}\)

I plotted y=2sin(2(x-pi))+1 in mathematica and it seemed to fulfill the requirements of the initial problem (e.g. period of pi, maxima in proper places, etc.), but I'd like someone else to confirm it.