Sine and Cosine Functions

For each real number t there corresponds an angle of t radians in standard position. We denote the point of interesection of the terminal side of the angle t with the unit circle by P(t). The x and y coordinates of this point give us the values of the six basic trigonometric functions. The y coordinate of P(t) is called the sine of t, while the x-coordinate of P(t) is called the cosine. The sine definition basically says that, on a right triangle, the following measurements are related the measurement of one of the non-right angles, the length of the side opposite to that angle and the length of the triangle's hypotenuse. Alternately, the cosine definition basically says that, on a right triangle, the following measurements are related: the measurement of one of the non-right angles, the length of the side adjacent to that angle and the length of the triangle's hypotenuse. Therefore cosine equals adjacent over hypotenuse and sine equals opposite over hypotenuse.