precalculus homework

Question

Find a possible formula for the trigonometric function whose values are in the following table.

x 0 2 4 6 8 10 12

y0 -4 -8 -4 0 -4 -8

y=

we didn't go over this in class so I'm really lost with it.

Answer 1

y = Acos(Bx + C) + D

The y-values fluctuate between -8 and 0, so the amplitude is 4 (half the distance between -8 and 0)

Let A = 4.

The midline is y = -4. Let D = -4.

There is no phase shift since y = 0 when x = 0(the maximum value of y on the cosine graph) Let C = 0.

y = 0 when x = 0 and y = 0 when x = 8

The period is 2π/B = 8. So let B = π/4

y = 4cos(π/4 x) - 4