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Transformations of Sine and Cosine 14 December 2010

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

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

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

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

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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,,,, )

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

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Example 1: y = -2 sin(t) – 2 t

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Example 2: t

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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.

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Cosine Graph cos(t) = x tcos t

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*Memorize: y = cos(t) tcos t

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

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

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

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Example 1: y = –cos(t) – 1 t

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Example 2: t

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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.

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6.5 COMBINING TRANSFORMATIONS 1. Multiple Inside Changes Example 2 (a) Rewrite the function y = f(2x − 6) in the form y = f(B(x − h)). (b) Use the result.

6.5 COMBINING TRANSFORMATIONS 1. Multiple Inside Changes Example 2 (a) Rewrite the function y = f(2x − 6) in the form y = f(B(x − h)). (b) Use the result.

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