In this article we shall indicate many different methods by which the sine and cosine functions may be defined. (From these the other four functions may be obtained by their usual definitions in terms of the sine and cosine functions, viz., cot θ = cos θ/sin θ.) In the course of the discussion we shall consider the trigonometric functions from various points of view and we shall list properties which are not to be found in standard texts on trigonometry but which are found in advanced mathematics. We shall also indicate some general applications which are inherent in these various methods and sources for other applications.