Construction of Sine and Cosine
The triangle inside the unit circle is a right triangle. The hypotenuse remains 1 as the base decreases and the height increases. Both the base and height remains under 1 except when the height is equal to 1, the point Q is on the y-axis and the base is equal to 1 when the point Q is on the x-axis. The area of the triangle changes and it proven when the point Q is on either axis giving the area 0. As the point Q moves counter-clockwise about the unit circle as it approaches the y-axis the height of the triangle gets closer to 1 and as it approaches to the x-axis it gets closer to 0. The opposite happens simultaneously to point A. The range of the y coordinate of Q is -1 to 1. The range of the y coordinate of A is 0 as A lies on the x-axis. The y-coordinate of point Q is used to create the sine graph. Is it the y value of the point Z. The arc length traversed by Q to the x-coordinates of A is the cosine curve.