Question

How do you find the amplitude, period, and shift for `y=1/3 sin (2x - pi/3)`?

Answer 1

See below.

Explanation:

If we write a trigonometric equation in the form:

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

Then:

Amplitude is a

Period is `(2pi)/b`

Phase shift is `(-c)/b`

Vertical shift is d

From example:

Amplitude `=a=1/3`

Period `= (2pi)/b=pi`

Phase shift `= (-c)/b=(pi/3)/2=pi/6`

Vertical shift `= d =0` no vertical shift.

Answer 2

`1/3,pi,pi/6,0`

Explanation:

`"the standard form of the sine function is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))`

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

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

`"here "a=1/3,b=2,c=-pi/3,d=0`

`rArr"amplitude "=|1/3|=1/3," period "=(2pi)/2=pi`

`"phase shift "=-(-pi/3)/2=pi/6`

`"there is no vertical shift"`