Follow the instructions in the questions and move the sliders for n, k and r in the applet accordingly. Answer the questions based on your observations.
Shift the slider value for n from n = 1 to n = 4. Describe the resultant transformation of y = cos(x) to y = cos(x - ¼π).
a translation by ¼π units in the positive x-direction
With the slider value of n kept at n = 4, shift the slider value for k from k = 1 to k = 2. Describe the resultant transformation of y = cos(x - ¼π) to y = cos(2x - ¼π).
a scaling parallel to the x-axis by a factor of 1/2
With the slider values of n and k kept at n = 4 and k = 2 respectively, shift the slider value for r from r = 1 to r = 3. Describe the resultant transformation of y = cos(2x - ¼π) to y = 3cos(2x - ¼π).
a scaling parallel to the y-axis by a factor of 3
What is the amplitude of y = r cos(kx - π/n), if r > 0?
What is the period of y = r cos(kx - π/n), if k > 0?
Describe a three-step transformation from y = cos(x) to y = cos(2x) - √3sin(2x).
[br]y = cos(2x) - √3sin(2x)[br] = 2cos(2x + π/3)[br][br]1. translate by π/3 units in the negative x-direction[br]2. scale parallel to x-axis by a factor of 1/2[br]3. scale parallel to y-axis by a factor of 2
What technique did you use in Question 8.6 to work out the three-step transformation?
Describe the replacement of variable in each step of your three-step transformation in Question 8.6.
1. Replace x by x + π/3.[br]2. Replace x by 2x.[br]3. Replace y by y/2.