# Sine Transformations

- Author:
- Peter Sassman

- Topic:
- Sine, Geometric Transformations

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.
Play around until you understand the idea, and then answer the questions below.

For all questions, consider the points

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