Question

What is the amplitude of `y=-2/3sinx` and how does the graph relate to `y=sinx`?

Answer 1

See below.

Explanation:

We can express this in the form:

`y=asin(bx+c)+d`

Where:

• `color(white)(88)bba` is the amplitude.
• `color(white)(88)bb((2pi)/b)` is the period.
• `color(white)(8)bb(-c/b)` is the phase shift.
• `color(white)(888)bb(d)` is the vertical shift.

From our example:

`y=-2/3sin(x)`

We can see the amplitude is `bb(2/3)`, amplitude is always expressed as an absolute value. i.e.

`|-2/3|=2/3`

`bb(y=2/3sinx)` is `bb(y=sinx)` compressed by a factor of `2/3` in the y direction.

`bb(y=-sinx)` is `bb(y=sinx)` reflected in the x axis.

So:

`bb(y=-2/3sinx)` is `bb(y=sinx)` compressed by a factor `2/3`in the direction of the y axis and reflected in the x axis.

Graphs of the different stages: