Tuesday 29 December 2015

trigonometry - Solving $sin 7phi+cos 3phi=0$




The question is find the general solution of this equation:$$\sin(7\phi)+\cos(3\phi)=0$$



I tried to use the "Sum-to-Product" formula, but found it only suitable for $\sin(a)\pm \sin(b)$ or $\cos(a)\pm \cos(b)$. So I tried to expand $\sin 7\phi$ and $\cos 3\phi$, but the equation became much more complicated..



I'm self studying BUT There's nothing about how to solve this type of equations on my textbook..



reeeaaaaally confused now..


Answer



Hint: Use sum to product!
$$\sin 7\phi+\sin \left(\frac{\pi}{2}-3\phi \right)=0$$



No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...