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MATHPOWER TM 12, WESTERN EDITION

Chapter 4 Trigonometric Functions. 4.4. Further Transformations of Sine and Cosine Functions. MATHPOWER TM 12, WESTERN EDITION. 4.4. 1. Transformations of Functions. The principles of transformations of functions apply to trigonometric functions and can be summarized as follows:.

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MATHPOWER TM 12, WESTERN EDITION

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  1. Chapter 4 Trigonometric Functions 4.4 Further Transformations of Sine and Cosine Functions MATHPOWERTM 12, WESTERN EDITION 4.4.1

  2. Transformations of Functions The principles of transformations of functions apply to trigonometric functions and can be summarized as follows: Vertical Stretch y = af(x) y = a sin x changes the to | a | Horizontal Stretch y = f(bx) y = sin bx changes the Vertical Translation y = f(x) + ky = sin x + k shifts the curve vertically k units when k > 0 and k units when k < 0 Horizontal Translation y = f(x - h) y = sin (x - h) shifts the curve horizontally h units when h > 0 and h units when h < 0 4.4.2

  3. Transforming a Trigonometric Function Graph y = sin x + 2 and y = sin x - 3. The range for y = sin x + 2 is The range for y = sin x - 3 is 4.4.3

  4. Transforming a Trigonometric Function A horizontal translation of a trigonometric function is called a 4.4.4

  5. Transforming a Trigonometric Function Sketch the graph of 4.4.5

  6. Analyzing a Sine Function p 2p Algabraic Solution y- intercept: x = 0 Domain: Range: Amplitude: Vertical Displacement: Period: Phase Shift: 4.4.6

  7. Analyzing a Sine Function In the equation of y = asin[b(x - c)] + d: a = 4, b = 3, d = -3, and Compare the graph of this function to the graph of y = sin x with respect to the following: a) equation b) amplitude d) phase shift c) period f) domain and range e) vertical displacement g)x- and y-intercepts 4.4.7

  8. Determining an Equation From a Graph A partial graph of a sine function is shown. Determine the equation as a function of sine. b = a = d = Therefore, the equation is . 4.4.8

  9. Determining an Equation From a Graph A partial graph of a cosine function is shown. Determine the equation as a function of cosine. b = a = d = . Therefore, the equation is 4.4.9

  10. Graphing Sine as a Function of Time The motion of a weight on a spring can be described by the equation Sketch this function. y = sin t The period is. The amplitude is. 4.4.11

  11. Assignment Suggested Questions: Pages 218 and 219 1-23 odd, 25-33, 34 (graphing calculator) 4.4.12

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