Write an equation for a function with the given characteristics. A cosine curve with a period of pi, and amplitude of 1, a left phase shift of pi, and vertical transiation up 5/2 of a unit.

y = cos (2x + 2π) - 5/2

Step-by-step explanation:

y = a cos (bx + c) + d

a = Amplitude = 1

period = 2π/b = π

b = 2

phase shift c/b = π

c/2 = π

c = 2π

vertical translation = 5/2 units

d = - 5/2 downwards

therefore substituting the values

y=1 cos (2x + 2π) - 5/2

y = cos (2x + 2π) - 5/2; equation for the function