It is a very convenient method to begin the study of Trigonometry with one or two lessons on Coordinates and the Coordinate Diagram. This leads to a general definition of the Sine and Cosine of any angle which the beginner has little difficulty in comprehending. With the help of the Coordinate Diagram the theorems on projection which are of so much importance can be proved with great precision. It is in such a course that the present proof of the Addition Theorems might find a place.