# Sine and Cosine Functions..

• October 28th 2008, 04:18 PM
zuuberbat
Sine and Cosine Functions..
Write an equation of the functions whose graphs are described in words below. Graph the functions. Identify the period, amplitude, and phase shift.

A) One cycle of y = sin x on [0, 2pi] is stretched to [0, 8pi] and then the stretched cycle is shifted horizontally pi/2 units to the right. The graph is also stretched vertically by a factor of 5/2 and then reflected in the x-axis.

B) One cycle of y = cos x on [0, 2pi] is stretched to [0, 8pi] and then the stretched cycle is shifted horizontally pi/2 units to the right. The graph is also stretched vertically by a factor of 5/2 and then reflected in the x-axis.

Explanations and steps would surely help. Thanks to anyone who spent their time to help!
• October 28th 2008, 06:14 PM
skeeter
A) One cycle of y = sin x on [0, 2pi] is stretched to [0, 8pi] and then the stretched cycle is shifted horizontally pi/2 units to the right. The graph is also stretched vertically by a factor of 5/2 and then reflected in the x-axis.

$y = -\frac{5}{2} \sin\left[\frac{1}{4}\left(x - \frac{\pi}{2}\right)\right]$

B) One cycle of y = cos x on [0, 2pi] is stretched to [0, 8pi] and then the stretched cycle is shifted horizontally pi/2 units to the right. The graph is also stretched vertically by a factor of 5/2 and then reflected in the x-axis.

you do this one.