Question

What is the difference between y=sinx and y = 4sinx when graphed?

Answer 1

Explanation:
Separately the periods for sin 4x and sin x are
π
2
and
2
π
.
The LCM =
2
π
is the period for the compounded oscillation
y
=
sin
4
x
−
4
sin
x
.
The second not-to-scale graph is for just one period
x
∈
[
−
π
,
π
]
.
graph{sin 4x - 4 sin x [-40, 40, -20, 20]}
graph{sin 4x - 4 sin x [-3.14, 3.14, -6.28, 6.28]}