Pre cal
posted by Angela .
a sinusoidal function has a local maximum at (0,2) and the next minimum at (Pi/4, 2). a correct equation for the function is

max at t = 0 is a cos function
y = A cos (k theta)
max is 2 so
y = 2 cos (k theta)
min of cos is at (k *pi/4) = pi radians
so k = 4
y = 2 cos (4 theta) 
Oh if they insist on sin rather than cos, use phase shift of pi/2
y = 2 sin (4 theta  pi/2) 
not pi/2 but +pi/2