December 4, 2012 Using Translations on Sine and Cosine Curves Warm-up: 1. What is the domain for ? 2.Write the equation, then state the domain and range.

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December 4, 2012 Using Translations on Sine and Cosine Curves Warm-up: 1. What is the domain for ? 2.Write the equation, then state the domain and range.

Lesson 4.5c Vertical and Horizontal Translations The sine and cosine curves follow the rules for vertical and horizontal translations of functions. Recall: y = (x – 3) 2 – 2 What would be the transformation for y = sin(x – π/3) – 2?

Horizontal Shift/Phase Shift What is the shift in this diagram?

General Equations for Translations of Sine and Cosine Curves Horizontal Shift or Phase Shift y = a sin(bx – c) + d and y = a cos(bx – c) + d, where a = b = c =

Sketch y = sin(x + π) 1.Identify the amplitude, period, and shifts.5. Reflections 2.Label the x- and y-axis.6. Vertical shifts 3. Sketch the original (with same amp) 4. Horizontal shifts

Vertical Shift What direction is this translation?

Vertical Shift y = a sinb(x +c) + d and y = a cosb(x + c) + d a = b = c = d = Identify the amplitude, period, and shift for: y = 2cos x – 1

Sketch y = 2cos x – 1 1.Identify the amplitude, period, and shifts.5. Reflections 2.Label the x- and y-axis.6. Vertical shifts 3. Sketch the original (with same amp) 4. Horizontal shifts

Use everything we have learned! Sketch y = 3cos (x – π/2) + 2

Classwork 4.5: Pg. 329 #45-48, 52-54, 63-66, 74