How to sketch $y=2\cos\,2x+3\sin\,2x$ , $x$ for $[-\pi,\pi]$. 
Use addition of ordinate to sketch the graph of  $y=2\cos\,2x+3\sin\,2x$  , $x$ for $[-\pi,\pi]$.

I know that there will be three line in graph from the example it show that
$x=0$, $x=\frac{\pi}{4}$, $x=\frac{\pi}{2}$ and something like that I haven't no clue how to do. Can you please explain in step by step, so that I'll be able to do other questions.
Answer look like this.
Thanks.!

I assuming you meant $\theta \in [-\pi,\pi]$, rather than $x$.
You might notice that $y = \sqrt{13} (\frac{2}{\sqrt{13}} \cos 2 \theta+\frac{3}{\sqrt{13}} \sin 2 \theta)$. Let $\alpha$ be the angle such that $\sin(\alpha) = \frac{2}{\sqrt{13}}$, and $\cos(\alpha) = \frac{3}{\sqrt{13}}$ (you should convince yourself that such an angle exists). Then the sum-product formulae for $\sin, \cos$ gives:
$$y = \sqrt{13} (\sin\alpha \cos 2 \theta+\cos\alpha \sin 2 \theta) = \sqrt{13} \sin(\alpha+2\theta).$$
You can compute $\alpha \approx 33.69^{\circ}$, plotting the function should be straightforward after that.
