I need help with consine function problem

Question

Find a cosine function (in standard form) that has the same graph as y = 4sin(0.5x-2π).

 

Thanks for answering.

Answer 1

Use the identity

 

sinθ = cos(π/2 - θ),

 

with θ in radians.

 

Then

 

sin(0.5x - 2π) = cos[π/2 - (0.5x - 2π)] = cos(-0.5x + 2.5π)

 

y = 4cos(-0.5x + 2.5π)