Question

Sketch the graph of the following pair of functions on the same axes:
$$f\left(x\right)=\sin x,g\left(x\right)=\sin (x+\frac{\pi }{4})$$

Answer 1

$$f\left(x\right)=\sin \frac{x}{2},g\left(x\right)=\sin x$$
Clearly, sin x and $$\sin (x+\frac{\pi }{4})$$ is a periodic function with period 2π.
The graphs of $$f\left(x\right)=\sin x\text{ and }g\left(x\right)=\sin (x+\frac{\pi }{4})$$ on different axes are shown below:


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