GRAPHS OF SINUSODIAL FUNCTIONS

A function is a sinusoid if it can be written in the form 

y = asin(bx – c) + d or y = acos(bx – c) + d, such that a, b, c, and d are constants, a ≠ 0 and b ≠ 0. 

• Where |a| is the amplitude of the curve and determines the vertical stretching or shrinking of the curve. 

• The value of b is used to calculate the period (2π/b) of the graph and is equal to the length of one full cycle of the wave.

• The value of c is used to calculate the determines phase shift (c/b) which is the horizontal shift of the curve along the x-axis.

• The value of d determines a vertical shift of the curve along the y-axis.  

Khan Academy Practice:

• Graphing the Sine Function

• Graphing the Cosine Function

• Calculating Amplitude

• Calculating Period