How to prove $\sin x$ is not a rational function?

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Today I encountered a question about a rational trigonometric function.

My thought: $\sin x$ doesn't give exact values like they are non-ending decimal number that's why it is like this. But in the second answer for that question that person told that rt2sinx is a rational trigonometric function, so how is it possible when rt2 is multiplied to it. In that answer rtsinx is there but I thought it won't make any difference. Please tell me whether I am going wrong somewhere (Like with my thoughts).