Question

How do you find the amplitude and period of `y=0.7tan(0.3x-1.8)`?

Answer 1

The amplitude does not exist/is undefined or however you want to say it. The period is `(20pi)/3`.

Explanation:

The equation can be written as `a sin(b(x-c)) + d`. For sin and cos (but not tan) `|a|` is the amplitude, `(2pi)/|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). In this case, you need to take out a `.3` inside of the parentheses. You then get `0.7tan(0.3(x-0.6))`. Now just follow the model above; the period is `(2pi)/.3` or `(20pi)/3`.
Note that tangent graphs do not have altitudes (they go from `-oo` to `oo`).