Question

How do you write an equation of the cosine function with amplitude 2, period pi, and phase shift pi/2?

Answer 1

`2cos(2x-pi)`

Explanation:

The standard form of the `color(blue)"cosine function"` is

`color(red)(bar(ul(|color(white)(a/a)color(black)(y=acos(bx+c)+d)color(white)(a/a)|)))`

where amplitude = | a | , period `=(2pi)/b`

phase shift `=-c/b" and vertical shift" =d`

here amplitude = 2 and d = 0

period `=(2pi)/brArrb=(2pi)/(pi)=2`

phase shift `=-c/brArrc=-2xxpi/2=-pi`

Thus equation is `y=2cos(2x-pi)`