If | B | > 1, | B | > 1, then the period is less than 2 ПЂ 2 ПЂ and the function undergoes a horizontal compression, whereas if | B | < 1, | B | < 1, then the period is greater than 2 ПЂ 2 ПЂ and the function undergoes a horizontal stretch. In the general formula, B B is related to the period by P = 2 ПЂ | B |. We can use what we know about transformations to determine the period. Looking at the forms of sinusoidal functions, we can see that they are transformations of the sine and cosine functions. Y = A sin ( B x в€’ C ) + D and y = A cos ( B x в€’ C ) + D y = A sin ( B x в€’ C ) + D and y = A cos ( B x в€’ C ) + D Determining the Period of Sinusoidal Functions Table 1 lists some of the values for the sine function on a unit circle. We can create a table of values and use them to sketch a graph. So what do they look like on a graph on a coordinate plane? LetвЂ™s start with the sine function. Recall that the sine and cosine functions relate real number values to the x- and y-coordinates of a point on the unit circle. In this section, we will interpret and create graphs of sine and cosine functions. In the chapter on Trigonometric Functions, we examined trigonometric functions such as the sine function. Light waves can be represented graphically by the sine function. The individual colors can be seen only when white light passes through an optical prism that separates the waves according to their wavelengths to form a rainbow. Instead, it is a composition of all the colors of the rainbow in the form of waves. White light, such as the light from the sun, is not actually white at all. Figure 1 Light can be separated into colors because of its wavelike properties.

Equation of a sine wave