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

Answer 1

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)

Answer 2

Oh if they insist on sin rather than cos, use phase shift of pi/2

y = 2 sin (4 theta - pi/2)

Answer 3

not -pi/2 but +pi/2