Question

Sketch the graph of the following pair of functions on the same axes:
\[f\left( x \right) = \sin\frac{x}{2}, g\left( x \right) = \sin x\]

Answer 1

\[f\left( x \right) = \sin\frac{x}{2}, g\left( x \right) = \sin x\]

Clearly, sin\[\frac{x}{2}\] and sin x is a periodic function with period 4π and 2π, respectively.
The graphs of f(x) = sin \[\frac{x}{2}\] and g(x) = sin x on different axes are shown below:

If these two graphs are drawn on the same axes, then the graph is shown below.