# How to create a coefficient matrix from a system with sin and cos functions

I'm struggling a bit. I want to create a coefficient matrix from a system of equations where there are some sinus terms in it. For example if I have the equations:

$$\sin(x_1) + 3x_2 + 4x_3 = 0$$ $$3x_1+ 5x_2+\cos(x_3)=0$$

So it's clear to me, that the coefficients 3 and 4 are in first row in my coefficient matrix, but what about the sinus term? Same in the second equation with the cosinus term. Will they be in the column vector with my x's?

In other words. How would my coefficient matrix and column vectors for this system look like respectively?

• You simply cannot do it. It's not a linear system, so it can't be represented as a matrix
– User
Feb 13, 2014 at 10:05
• @Matteo: ah thanks, I didn't know that. How would one normally analyze such a system? Feb 13, 2014 at 10:18
• I don't know if there is a standard way of doing it. Sorry, but i don't even know how to start
– User
Feb 13, 2014 at 10:27
• @Matteo: Any links or some information to read up on? Feb 13, 2014 at 10:32
• No, unfortunately I don't know where you can look for an answer to this
– User
Feb 13, 2014 at 10:39

Unfortunately, it is trigonometric system, not a linear one. Hence it cannot be expressed into the $Ax=b$ form.
Try to put it in this way: $$\sin(x1)=-(3x_2+4x_3); \\ \cos(x_3)=-(3x_1+5x_2);$$ Hence: $$(3x_2+4x_3)\in[-1,1]; \\ (3x_1+5x_2)\in[-1,1];$$ Try to verify the solvability of the system by verifying those conditions (if those are not verified the system is not compatible, otherwise you should try other ways).