Question

How do you write an equation for a cosine function with an amplitude of 2/3, a period of pi, and a vertical shift of 2 units up?

Answer 1

Equation is `color(indigo)(y = 2/3 cos(2x) + 2`

Explanation:

Standard form of the cosine function is `y = A cos(Bx - C) +D`

Amplitude `= |A| = 2/3`

Period `= (2pi)/|B| = pi`

`:. B = 2`

Phase Shift `= -C / B = 0`

Hence `C = 0`

Vertical Shift `= D = 2`

Hence the equation is `color(indigo)(y = 2/3 cos(2x) + 2`

graph{2/3 cos (2x) + 2 [-10, 10, -5, 5]}