Question

What is the period, amplitude, and frequency for the graph `f(x) = 1 + 2 \sin(2(x + \pi))`?

Answer 1

The general form of the sine function can be written as

`f(x) = A sin(Bx +- C) +- D`, where

`|A|` - amplitude;
`B` - cycles from `0` to `2pi` - the period is equal to `(2pi)/B`
`C` - horizontal shift;
`D` - vertical shift

Now, let's arrange your equation to better match the general form:

`f(x) = 2 sin(2x +2pi) +1`. We can now see that

Amplitude -`A` - is equal to `2`, period -`B` - is equal to `(2pi)/2` = `pi`, and frequency, which is defined as `1/(period)`, is equal to `1/(pi)`.