Question

How do you write the equation of the cosine function with an amplitude of 2 and a period of 3pi/5?

Answer 1

`y=2cos(10/3x)`

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| and period`=(2pi)/b`

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

here amplitude = 2 and period `=(3pi)/5`

`rArrb=(2pi)/((3pi)/5)=2cancel(pi)xx5/(3cancel(pi))=10/3`

`rArry=2cos(10/3x)" is the equation"`