Question

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

Answer 1

amplitude = 2
period `=2pi`

Explanation:

For the standard `color(blue)"sine function"`

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

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

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

here a = -2 , b = 1 , c `=pi/2" and d = 0"`

Hence amplitude = |-2| = 2 and period `=(2pi)/1=2pi`