Algebra Question

Question

Write an equation for a cosine function with a amplitude of 5, a period of 6, a phase shift of 1, and a vertical displacement of 1.

A. y= cosπ(x-5)+6

B. y= 6cos5π(x-1)+1

C. y= 5cos3π(x+1)-1

D. y= 5cos2π(x-1)/6+1

Answer 1

y = A cos[(2π/T)(x - φ)] + y₀

A = amplitude = 5

T = period = 6

φ = phase shift = 1

y₀ = vertical displacement = 1

Plug in the values and get

y = 5 cos[(2π/6)(x - 1)] + 1

It looks like (D) is the right answer.