Question

Given any sinusoidal equation, how do you identify the type of transformations that are made?

Answer 1

Example: Describe the transformations to get `g(x) = 2sin(3(x + pi/4)) + 2` from `f(x) = sinx`

Here are what each of the parameters in the equation `y = asin(b(x -c)) + d`:

`a ->` vertical stretch
`1/b ->`horizontal stretch
`c ->` phase shift
`d ->`vertical transformation

So in the given equation, we have a vertical stretch by a factor of `2`, a horizontal stretch by a factor of `1/3`, a transformation `pi/4` units left and a transformation `2` units up.

Hopefully this helps!