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In analytic geometry a linear function means a first-degree polynomial function of one variable. These functions are called "linear" because their graphs in the Cartesian coordinate plane are a straight lines.

A sine wave does not have a graph that is a straight line.

A linear equation would imply meeting of superposition, that is af(x) + bf(y) = f(ax+by). We know from basic trig that sin(a+b) = sin(a)cos(b) + cos(a)sin(b). We can derive this out and find that sin(a+b) is not the same as sin(a) + sin(b).

This therefore would exclude sin from being linear either in the geometric or systems sense.

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Are linear equations and functions the same?

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