Data Loading...
Amplitude and Vertical Dilation of Sine and Cosine Functions Flipbook PDF
Worksheet: Amplitude and Dilation of Sine and Cosine Function Nicholas Bennett & LFS Precalculus with Trigonometry 3
143 Views
114 Downloads
FLIP PDF 56.89KB
Worksheet: Amplitude and Dilation of Sine and Cosine Function
Nicholas Bennett & LFS
Amplitude and Vertical Dilation of Sine and Cosine Functions In this activity, you will discover the relationship between the vertical dilation A and the amplitude of: y A sin( x ) and y A cos( x ) Applet: Amplitude_Vertical_Dilation Terminology: Vertical dilation stretches or compresses the function along the y-axis.
Before you begin, check that: A=1 and that the checkbox “Allow Fractions for A” is unchecked.
Questions and Answers: 1. Write down the parent functions of y A sin( x ) and y A cos( x ) . What is the value of A and what is the amplitude of these parent functions? Answer: Parent functions are y = sin(x) and to y = cos(x), respectively. In both parent functions, the value of A is 1 and the amplitude=1. 2. Move slider A in any direction (A 0). What type of transformation does this represent? Answer: Moving A (A 0) in any direction gives a vertical dilation or (since |A|>1), the transformation is a vertical stretch. 3. What happens to y = Asin(x) and to y = Acos(x) when A increases in the positive direction? Answer: When A increases in the positive direction and since A>1, the functions stretch vertically more and more. 4. Set A = 2. Write the equations for both the sine and cosine functions below. Answer: The equations are y = 2sin(x) and y = 2cos(x).
Precalculus with Trigonometry
1
Worksheet: Amplitude and Dilation of Sine and Cosine Function
Nicholas Bennett & LFS
5. What is the amplitude of both sine and cosine under this vertical dilation? Answer: The amplitudes of y = 2sin(x) and y = 2cos(x) is amplitude=2. 6. Set A = 4. Write the equations for both the sine and cosine functions below. Answer: The equations are y = 4sin(x) and y = 4cos(x). 7. What is the amplitude of both sine and cosine under this vertical dilation? Answer: The amplitudes of y = 4sin(x) and y = 4cos(x) is amplitude=4. There seems to be a relationship between the amplitude of a sinusoidal function and A. Let's see if you can see the pattern. Table 1: Positive Whole Numbers for A.
Dilation Factor
A=1
A=2
A=4
Amplitude
amplitude = 1
amplitude = 2
amplitude = 4
8. Write an equation for the amplitude in terms of A when A>0. Answer: The amplitude of the functions y = Asin(x) and to y = Acos(x) is amplitude=A. Note: Because we are not looking at A1, the functions y = Asin(x) and y = Acos(x) are stretched compressed and the amplitude A of these functions is amplitude > 1 amplitude < 1. 3. When the amplitude < 1 of the functions y = Asin(x) and y = Acos(x), this means that |A|>1 0