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14.2 Translations and Reflections of Trigonometric Graphs

14.2 Translations and Reflections of Trigonometric Graphs. Algebra 2. Graphing Sine and Cosine Functions. To obtain the graph of y = a sin b(x – h) + k or y = a cos b(x – h) + k transform (move) the graphs of y = a sin bx or y = a cos bx as follows.

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14.2 Translations and Reflections of Trigonometric Graphs

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  1. 14.2 Translations and Reflections of Trigonometric Graphs Algebra 2

  2. Graphing Sine and Cosine Functions • To obtain the graph of y = a sin b(x – h) + k or y = a cos b(x – h) + k transform (move) the graphs of y = a sin bx or y = a cosbx as follows. • Vertical Shift- Shift the graph k units vertically • Horizontal Shift – Shift the graph h units horizontally • Reflection- If a<0, reflect the graph in the line y=k after the vertical and horizontal shifts

  3. Examples: • Write an equation for the graph describing the following. • The graph of shifted up 4 units. • The graph of shifted left 4 units. • The graph of reflected over the x-axis.

  4. More Examples

  5. Examples: • Graph • Graph • Graph y=-cos4x

  6. Example: • Graph

  7. More Examples:

  8. Example: • Give the amplitude, period, and five key points of the graph of

  9. Example: • You are riding a Ferris wheel. You height h (in feet) above the ground at any time t (in seconds) can be modeled by the equation: The Ferris wheel turns for 160 sec before it stops to le the first passenger off.

  10. Example (continue) • Sketch the graph of your height with respect to t. • What are your minimum and maximum heights?

  11. Example: • On another Ferris wheel, your height s given by the equation • How many cycles will this Ferris wheel make in 150sec? • What are your maximum and minimum heights? • What is you height after 150sec?

  12. Graphing Tangent Functions • To obtain the graph of y = a tan b(x – h) + k, transform y = a tan bx as follows • Shift the graph k units vertically and h units horizontally. • Then, if a<0, reflect the graph in the line y=k.

  13. Examples: • Graph • Give the asymptotes, the halfway points, and center points of the graph of y=2 – 3tan 2x

  14. More Examples:

  15. Example: • You are standing 90 ft from where a balloon was launched. The balloon travels straight up to a maximum height of 120 ft. What is the angle of elevation of the balloon when it is 50 ft from the maximum height?

  16. Example: • A balloon is launched 150 ft away from you. It can reach a maximum height o 200 ft. What is the angle of elevation of this balloon when it is 80 ft from the maximum height?

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