The trigonometric functions in the four quadrants.
After the demonstration of the formulas of addition and subtraction for sine and cosine in the first quadrant, the proof of the validity in the four quadrants is often omitted. As the visual understanding with the unit circle would be complex, the proof is done only with expressions. The trigonometric functions have the nature that can represent the values in the second quadrant, the third quadrant and the fourth quadrant by the values that are in the first quadrant..
