# 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?

Jul 25, 2018

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

#### Explanation:

Standard form of the cosine function is $y = A \cos \left(B x - C\right) + D$

Amplitude $= | A | = \frac{2}{3}$

Period $= \frac{2 \pi}{|} B | = \pi$

$\therefore B = 2$

Phase Shift $= - \frac{C}{B} = 0$

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]}