The applet below has 4 different transformations of the curve, y=sin x. You can cycle through them, by pushing "Next Transformation", and move the sliders for a,b,c, and d. Note: x is in radians.[br][br]Play around until you understand the idea, and then answer the questions below.

For all questions, consider the points [b]minimum, maximum, amplitude, principal axis, period[/b].[b][br][br]Question 1: (a sin x) [br][/b]a. Change a. What changes, and what stays the same?[br]b. How does a affect the function y=a sin x?[br]c. Choose three different a values, and write down the minimum, maximum, and amplitude.[br]d. Hence, what is the amplitude of y=3.56sin x? y=-4sin x? y=a sin x?[br][br][b]Question 2: (sin (bx)) [br][/b]a. Change b. What changes, and what stays the same?[br]b. How does b affect the function y=sin (bx)?[br]c. Choose three different b values, and write down the periods.[br]d. Hence, what is the period of y=sin (3x)? y=sin (1/2 x)? y=sin(bx)?[br][br][b]Question 3: (sin (x-c)) [br][/b]a. Change c. What changes, and what stays the same?[br]b. How does c affect the function y=sin (x-c)?[br][br][b]Question 4: (sin x + d) [br][/b]a. Change d. What changes, and what stays the same?[br]b. How does d affect the function y=sin x + d?[br]c. Choose three different d values, and write down the equations of the principal axis.[br]d. Hence, what is the principle axis of y=sin x + 5? y=sin x - 3? y=sin x + d?[br][br][b]Question 5: (General Case)[br][/b]From previous questions, find the minimum, maximum, period, principal axis, and amplitude, of the function [br]y=a sin(b(x-c))+d.