Question

How do you find the amplitude, period, and shift for `y= -sin (4/3)x`?

Answer 1

amplitude`=1`
period`=270^@`
phase shift`=`none
vertical shift`=`none

Explanation:

The general equation for a sine graph is:

`y=color(red)asin(color(orange)k(x-color(green)d)+color(blue)c`

where:
`color(red)a=|"amplitude"|`
`color(orange)k=360^@/("period")`
`color(green)d=`phase shift
`color(blue)c=`vertical shift

In this case, since the value of `a` is `1`, the amplitude is `1`. It would not be `-1` because the amplitude is always an absolute value, or always positive.

The period is found by substituting the `k` value, `4/3`, into the equation, period`=360^@/k`:

period`=360^@/k`
`=360^@/(4/3)`
`=360^@-:4/3`
`=360^@*3/4`
`=color(red)cancelcolor(black)(360^@)^(90^@)*3/color(red)cancelcolor(black)4`
`=270^@`

The phase shift is `0` in this case since there is no indication after the `x` variable in the equation.

The vertical shift is `0` in this case since there is no indication at the end of the equation.