How is the midline used to help graph trigonometric functions and what is the definition of phase shift for sine and cosine?
The midline is a horizontal axis that is used as the reference line about which the graph of a trigonometric function oscillates.
Graph 1 shows y= sin x and Graph 2 shows y= sin x + 1. The second curve is the first curve shifted vertically up by one unit. The midline of y = sin x is the x-axis and the midline of y= sin x + 1 is the line y = 1.
The equation of the midline of trignometric function is the average of the maximum and minimum values of the function i.e. y=(min. + max.)/2.
Phase shift is the amount of horizontal displacement of the trigonometric function from its original position.
The general form of the sine function is y=Asin(Bx-C)+D and the cosine function is y=Acos(Bx-C)+D
The phase shift of the functions is given by C/B. A positive phase shift means the graph has moved to the right, while a negative phase shift means the graph has moved to the left.
Cosine functions are identical to the sine functions, except that they are phase shifted to the left by 90°. By accounting for this shift, any sine function can be written as a cosine function, and any cosine function can be written as a sine function.