Question

How do you find the amplitude, period, and shift for `y = 2sin (2x - pi) +1`?

Answer 1

`2 , pi,-pi`

Explanation:

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

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

where amplitude = |a| , period`=(2pi)/b` , c is the phase shift and
d, the vertical shift.

here amplitude = |2| = 2 , period`=(2pi)/2=pi`

phase shift `=-pi" and vertical shift "=((0),(1))`