1. Transformations of Sine and Cosine 14 December 2010

2. Stretch v. Compression Stretch = Fraction!!! Compression = Not a Fraction!!!

3. Transformations f(x) = a sin(bx – c) + k Vertical Shift Stretch or Compression Period Shift Horizontal Shift Pay attention to the parentheses!!!

4. Examples Stretch/Compression: Horizontal Shift: Vertical Shift: Stretch/Compression: Horizontal Shift: Vertical Shift:

5. Your Turn: On the “Transformations of Trigonometric Functions” handout, complete Part A for questions 1 – 4.

6. Sketching Transformations Step 1: Graph the parent equation Step 2: Identify the correct order of operations for the function Step 3: Make a table that follows the order of operations for the function Step 4: Complete the table for the key points (0,,,, )

7. *Memorize: y = sin(t) tsin(t)

8. Example 1: y = -2 sin(t) – 2 t

9. Example 2: t

10. Your Turn: On the “Transformations of Trigonometric Functions” handout, complete Parts B and C for problems 1 – 4. On the “Transformations of Trigonometric Functions” handout, complete Parts D – F for problems 1 – 4.

11. Cosine Graph cos(t) = x tcos t

12. *Memorize: y = cos(t) tcos t

13. Transformations f(x) = a cos(bx – c) + k Vertical Shift Stretch or Compression Period Shift Horizontal Shift Pay attention to the parentheses!!!

14. Cosine Examples Stretch/Compression: Horizontal Shift: Vertical Shift: Stretch/Compression: Horizontal Shift: Vertical Shift:

15. Your Turn: On the “Transformations of Trigonometric Functions” handout, complete Part A for problems 5 – 8.

16. Example 1: y = –cos(t) – 1 t

17. Example 2: t

18. Your Turn: On the “Transformations of Trigonometric Functions” handout, complete Parts B and C for problems 5 – 8. On the “Transformations of Trigonometric Functions” handout, complete Parts D – F for problems 5 – 8.