Question

How do you find the amplitude and period of a function `y = 5+3sinx`?

Answer 1

The amplitude is 3 and the period is 2`pi`. (The phase shift is (0, 5) if you wanted to know).

Explanation:

The equation can be written as `asin(b(x−c))+d` (or in your case `d + asin(b(x-c))`. For sin and cos (but not tan) `|a|` is the amplitude, `(2π)/|b|` is the period, and `c` and `d` are the phase shifts. `c` is the phase shift to the right (positive `x` direction) and `d` is the phase shift up (positive `y` direction). Hope this helps!