Transformation of the trigonometric functions

Select any one or more of the trigonometric function to see how they are transformed by four constants, a, b, c, and d. In general the transformations can be represented as: f1(x) = c + a f(b (x - d)). c is the vertical translation. d is the phase shift, or horizontal translation. b is reciprocally related to the horizontal dilation, which affects the period of the functions, and a is the amplitude or vertical dilation. Note that all six trig functions are affected in similar ways by these six transformations.