Solving simple symbolic trigonometry equations

I have a simple trigonometric equation I would like to solve, but I can't seem to get Matlab to give me an answer:

a*sin(x)-b*cos(x) = 0

I want to solve for x. This has a trivial solution and is easy to see by eye:

x = atan(b/a) and x = atan(b/a) + pi

I'd like to know whether it's possible to lead Matlab to the answer. I've tried:

syms a b x real;
solve(a*sin(x)-b*cos(x) == 0,x) % No solution
solve(a*sin(x) == b*cos(x),x) % Again, no solution
solve(a*sin(x)-b*cos(x), x) %Again no solution

All of these (and the variations I've thought of) give no solution. Any thoughts?

Answer 1

[Vineeth Kartha]

Hi John,

Use the "solve" command as follows:

>> solve(a*sin(x) == b*cos(x),x,'IgnoreProperties',true,'ReturnConditions',true);

This returns a structure expressing the full solution.

Refer to the MATLAB documentation of solve for more information.

[John]

Hmm. Thanks for your answer. I had come across that combination, which for the sake of any other readers gives:

pi*k - (log((a + b*1i)/(a - b*1i))*1i)/2

However I was really hoping to avoid complex exponentials in the the answer (it complicates subsequent manipulation). All my variables are real-valued, and carrying along the full complex form is cumbersome.