Vertical Translations

Question

Find a cosine equation having the following characteristics:

amplitude= 2

period= 8pi

horizontal shift= 4pi

vertical shift= -2

Thank you in advance!

Answer 1

The equation has the form y = Acos(Bx + C) + D

Vertical shift = D = -2

Amplitude = lAL = 2 (Let A = 2)

Period = 2π / lBl = 8π. So, lBl = 1/4. Let B = 1/4

Horizontal shift = -C/B = -4C = 4π. C = -π

y = 2cos(x/4 - π) - 2