Question

How do you graph `y=-2 - 3 sin (x - pi)`?

Answer 1

See the inserted graph and the explanation.

Explanation:

`y=-2-3 sin (x-pi)=-2+3 sin (pi-x)=-2+ 3 sin x`

The period `2pi` for sin x is the period of y..

The graph is symmetrical about (0. -2).

So, a Table for the half period `x in [0, pi]` is sufficient for extending

it for one period `x in [-pi. pi]`.

`(x, y): (0, -2) (pi/6, -3/2) (pi/3, 3sqrt3/2-2) (pi/2, 1)`

`(2/3pi, 3sqrt3/2) (5/6pi, =3/2) (pi, -2)`

The crests of f the periodic wave in the graph are at

`(-3/2pi, 1), (pi/2, 1) and (5/2pi, 1)`.

graph{y=3 sinx -2 [-10, 10, -5, 5]}