math 1730
Bella edwards
MathDiscussions.docxPart 1: You will explore the amplitude and period of the sine and cosine functions using the Guided Visualization found at Amplitude and Period of Sine and Cosine Functions.
Select the sine function and move one variable slider at a time and observe how the function changes. Select the reset button and investigate the cosine function.
Answer each of the following questions in your Initial Posting.
1. How does changing the value of A affect the graph of the sine and cosine function?
2. How does changing the value of A from positive to negative affect the graph of the sine and cosine function?
3. How does changing the value of B affect the sine and cosine functions?
Example
1) How does changing the value A affect the graph of the sine and cosine function?
As we learned in this unit, A, is the amplitude of the wave created by the function(s). The larger the value of A, the larger the height of the wave. Similarly, the smaller the value of A, the smaller the height of the wave. This relationship applies to both the sine and cosine functions.
(2) How does changing the value A from positive to negative affect the graph of sine and cosine?
Changing the value of A from positive to negative will not change the wave in the same way as the larger or smaller value discussed above would, rather it shifts the position of the wave on the graph across the axis.
(3) How does changing the value of B affect the sine and cosine functions?
As we learned, B is the period of the cycle of the wave. Thus changing the value of B will affect the length of the graphs period/ how far it goes along the x-axis. The higher the value of B, the more compact/steeper the wave will be. This relationship applies to both the sine and cosine functions!
