Translations:Sinusoidal motion/13/en

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At time n = 0, the vector lies in the positive direction along the horizontal coordinate axis. Then at some arbitrary time index n, the vector will make an angle of radians with the horizontal axis. The projections of this vector on the x- and y-axes give the horizontal and vertical components, respectively: . Let the vertical axis be the imaginary axis (i.e., a unit distance on the vertical axis is ). We can represent the vector at time in terms of its components and as follows: