(1) Plot the graph of the function $y=f(x)$ where $f(x) = \sin x +\sin x$. Find the first derivative of this function and say where it is defined and where it is not defined.
(2) Express the function $f(x) = \sin x + \cos x$ in the form $f(x)=A\sin (x+\alpha)$, find $A$ and $\alpha$ and plot the graph of this function. Similarly express the function $g(x) = \sin x  \cos x$ in the form $g(x) = B\sin (x +\beta)$ where $\pi /2 < \beta < \pi /2$, and plot its graph on the same axes.
(3) Plot the graph of the function $y=f(x)$ where $f(x)= \sin x + \cos x$. Find the first derivative of this function and say where it is defined and where it is not defined.
