So, my question is really simple. What are the requirements for a1, a2, C1, C2 for a real solution to exist for the following system of equations?(adsbygoogle = window.adsbygoogle || []).push({});

sin(theta1) + a1*sin(theta2) = C1

cos(theta1) + a2*cos(theta2) = C2

If it would be helpful, I'm not interested in the solution, necessarily (could do that with numerical methods), just interested for what parameter configurations it exists over real numbers.

I have tried assuming a complex solution and then imposing conditions on that but it hasn't really taken me anywhere...

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# When does a real solution exist for this system of trigonometric equations?

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