Question

How do you write the equation of the sine function with an amplitude of 1/9 and a period of 3pi?

Answer 1

`y=1/9sin(2/3x)`

Explanation:

The standard form of the sine function with period `p=(2pi)/b` and amplitude `a` is given by

`y=asin(bx)`

First, we'll need to solve for `b.` We're given `p=3pi.` Moreover, since `p=(2pi)/b,`

`3cancelpi=(2cancelpi)/b`

`b=2/3`

We're given `a=1/9.` The amplitude must be positive -- this is already positive, so no worries, but were it not positive, we'd need to take the absolute value.

Thus, we have

`y=1/9sin(2/3x)`