Question

How do you graph `y = sin4x - 4 sin x`?

Answer 1

See explanation and graphs.

Explanation:

Separately the periods for sin 4x and sin x are `pi/2 and 2pi`.

The LCM = `2pi` is the period for the compounded oscillation

`y = sin 4x-4 sin x`.

The second not-to-scale graph is for just one period `x in [-pi, pi]`.

graph{sin 4x - 4 sin x [-40, 40, -20, 20]}

graph{sin 4x - 4 sin x [-3.14, 3.14, -6.28, 6.28]}