## System of Equations solutions

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

### System of Equations solutions

Hello, how do I go about solving this system of equations? Angle measurements are in radians. I will need to use this method again for many values other than 660 in the second sine function. For reference, I'm using this method to find the wavelength of the function $f(x) = \sin{(2\pi440x)} + \sin{(2\pi660x)}$

This is the system.
$\sin{(2\pi440x)} = \sin{(2\pi660x)}$
$\sin{(2\pi440x)} = 0$
$\sin{(2\pi660x)} = 0$

Thank you for your help.
Phantom Wings

Posts: 1
Joined: Fri Nov 01, 2013 12:12 am

### Re: System of Equations solutions

The sines are 0 when their arguments are multiplies of (pi), so 2(pi)660x = n(pi) so 2*660*x = n. The same for the other sine. When they're equal you can subtract to get them on the same side. Then do the identity sin(a)-sin(b) = 2cos((a+b)/2)sin((a-b)/2). This is zero when the cosine or the sine is zero. The system is solved wherever all three formulas for the arguments are the same.

Posts: 79
Joined: Sun Feb 22, 2009 11:12 pm