Question

The graph of a cosine function has amplitude = 3, period = 90 degrees, and a vertical translation 2 units up. Write an equation for the function. Then sketch the graph.

Answer 1

If a cosine function has amplitude of A, and a period of T, shifted up K units, the equation is

y = A cos(bx) + K

Now period is given by T = 2pi/b so b = 2pi/T
So sub in your amplitude, b and your K into the formula.

Answer 2

as I see you are using degree measure rather than radians, you can use T = 360/b instead
so b = 360/T