# Solutions of trigonometric equation $a\sin(x) + b\cos(x) = n$

Is there a solution of the equation $a\sin(x) + b\cos(x) = n$ in rational numbers (i.e. $a,b,n,x$ are rational and positive) where $x$ is not of the form $90n^\circ$?
(This question was also there on https://math.stackexchange.com/questions/1290626/integer-solutions-of-equation-sin-x-cos-x-n but it seems to have been blocked)
Edit: Basically, I just want an example where two irrational trigonometric ratios add up to give a rational number. But if x itself is irrational I cannot expand the functions of $sin$ and $cos$ properly. Hence I am looking for rational solutions of x. ($a$ and $b$ are optional i.e., they can be omitted. I just gave them in the hope that it would expand the answer set)
I am just a beginner to trigonometry.

• Did you read why the former posting of the same question was closed? "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." Without addressing what was pointed out as a problem with the other post, this post will soon meet the same fate. – JMoravitz May 21 '15 at 1:47
• hmm... alright. – SS_C4 May 21 '15 at 1:48
• Any more information to be provided? – SS_C4 May 21 '15 at 1:58
• It is better, but still doesn't address the issue of "what do you understand about the problem already" and "what attempts have you made to solve it." For clarification, you require $a,b,n$ to be rational numbers and $x$ can be any real number? Or do you require $x$ to be rational as well? Rational in terms of degrees or in terms of radians? – JMoravitz May 21 '15 at 2:00
• May be of interest: mathworld.wolfram.com/NivensTheorem.html – Ramashalanka May 21 '15 at 2:14