Periodic processes, sine and cosine

On a circle of radius 1, rotate the point (1, 0) about the origin by an angle α: the ordinate of the resulting point is sin α and its abscissa is cos α. Because the point lies on the circle, sin²α + cos²α = 1 (the fundamental trigonometric identity). Angles are also measured in radians: 180° = π rad, so α° = α · π/180 radians; for example 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2. Special values: sin 30° = 1/2, cos 30° = √3/2, sin 45° = cos 45° = √2/2, sin 60° = √3/2, cos 60° = 1/2; sin 90° = 1, cos 90° = 0. In the second quadrant sin(180° − α) = sin α and cos(180° − α) = −cos α, because the points are symmetric about the y-axis. y = sin x and y = cos x have period 2π, amplitude 1 and values in [−1, 1]. For y = a sin bx + c the amplitude is |a|, the period is 2π/|b| and the midline is y = c.