Is x*cos(Ax) + B*sin(Ax) = 0 Solvable for x?

[Michael12345]

Homework Equations

x*cos(Ax) + B*sin(Ax) = 0

Where A and B are nonzero constants.

The Attempt at a Solution

The only value of x where both terms are zero is x=0. All other solutions (presumably an infinite number of them) occur when:

x*cos(Ax) = -B*sin(Ax), x≠0.

This seems intractable to me, but I don't have the math skills required to recognize an equation that cannot be solved algebraically.

 

[tiny-tim]

Hi Michael!

x*cos(Ax) = -B*sin(Ax), x≠0.

This seems intractable to me, but I don't have the math skills required to recognize an equation that cannot be solved algebraically.

You can simplify it as tan(Ax)/x = -1/B …

yes, that has no algebraic solution.