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

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]}