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January 4th, 2018, 09:32 AM   #11
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One definition of sine (and cosine) commonly used in Calculus texts is this: Set up a coordinate system with the unit circle, the graph of $x^2+ y^2= 1$. Starting at (1, 0), measure around the circumference a distance t. The coordinates of the end point are, by definition, (cos(t), sin(t)). In that case, t has no units because its length is just a multiple of the unit used in the coordinate system. The "radian" measurement is defined to fit that.
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