If P is minimum at 600 and maximum at 1300, this represents a sine value of -1 at t=0 and a sine value of +1 at t=6 (months). So we need a phase shift of 90 degrees or (pi)/2 so that at t=0 we have the sine of -(pi)/2 which is -1. So we're looking at sin(t-90) or sin(t-(pi)/2). The amplitude of the sine wave is 2 (-1 to 1 has a range of 1-(-1)=2). The difference between the low and high P values is 1300-600=700, so we need to multiply the sine by 350 to achieve this range between the minimum and maximum, and we get that through 350sin(t-(pi)/2), which gives us a number between -350 and +350. But the minimum is 600 so we need to add something to -350 to make 600, and that means we have to add 950 because 950-350=600. Now we have 950+350sin(t-(pi)/2), when t=0, this comes to 600. Fine. But when t=6 we need P to be 1300, and we have 950+350sin(6-(pi)/2)=1300. What's missing? It's the wavelength. We know the sine argument has to be (pi)/2. Therefore 6x-(pi)/2=(pi)/2 or 6x=(pi) and x=(pi)/6=30 degrees. Now the equation becomes P=950+350sin((pi)(t/6-1/2). What is P when t=12? sin(3(pi)/2)=-1 so P=950-350=600. So we have a complete oscillation back to the minimum at Jan 1, and the equation is confirmed. It can be written:
P=950+350sin(((pi)/6)(t-3))