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Most branches of mathematics - including trigonometry - deal with numbers. The square root of three is a number.
You cannot convert even numbers to triangular numbers! There is no such relationship.
The domain of cosine is all real numbers, its range is [-1,1], and its period is 2π radians.
Putting a question mark at the end of a phrase does not make it a sensible of even an answerable question. Sine and cosine of real numbers? Yes, they do exist. In fact, sines and cosines of complex numbers also exist. Does that answer the question?
No. Triangle numbers are a fixed set of numbers that can't be altered to make one certain number turn into a triangle number.