a cos curve with a period8pi, an amplitude2, a right shift pi/2, and a vertical translation5 units up.

Question

Write an equation for the function. My answer was 1cos(1/4x-pi/8)+5 and that i am told that it is not the right answer.

Answer 1

The standard form of the cosine function is

y  =  a cos (bx + c) + d ------------------------> (1)

Amplitude :  a = 2

Vertical shift :  d = 5

Period :  2π/b = 8π

               b = 2π/8π

               b = 1/4

Phase Shift :   -c/b  =  π/2

                       -c/(1/4)  =  π/2

                       -c  =  (π/2)(1/4)

                       -c  =  π/8

                        c  =  - π/8

Substitute Corresponding values in Eq (1)

y  =  2 cos (x/4 - π/8) + 5

Answer:

y  =  2 cos (x/4 - π/8) + 5.