1 / 44

5.6 Transformations of the Sine and Cosine Graphs Mon Feb 3

5.6 Transformations of the Sine and Cosine Graphs Mon Feb 3. Do Now Use the sine and cosine values of 0, pi/2, pi, 3pi/2 and 2pi to sketch the graph of f(x) = sin x and g(x) = cos x. Review of graphs. Y = sin x Period of 2pi Amplitude of 1 Goes through (0, 0). Review of Graphs.

dyami
Download Presentation

5.6 Transformations of the Sine and Cosine Graphs Mon Feb 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 5.6 Transformations of the Sine and Cosine GraphsMon Feb 3 Do Now Use the sine and cosine values of 0, pi/2, pi, 3pi/2 and 2pi to sketch the graph of f(x) = sin x and g(x) = cos x

  2. Review of graphs • Y = sin x • Period of 2pi • Amplitude of 1 • Goes through (0, 0)

  3. Review of Graphs • Y = cos x • Period of 2pi • Amplitude of 1 • Goes through (0, 1)

  4. Transformations • We are interested in the graphs of functions in the form

  5. The Constant A • Recall that coefficients of functions result in a vertical shift / shrink • The constant A affects the amplitude of sine and cosine. The amplitude = A • If A is negative, the graph is upside down

  6. Ex • Graph the following • 1) • 2) • 3)

  7. The Constant B • Recall that coefficients of X result in a horizontal stretch / shrink • The constant B affects the period • The period of these graphs is

  8. Ex • Sketch a graph of the following • 1) • 2)

  9. The Constant C • The constant C, like in previous functions, results in a horizontal shift C units right / left • This is also known as a phase shift • Ex: sin (x – 4) is a shift to the right 4 units • Cos (x + pi) is a shift to the left pi units

  10. The Constant D • The constant D results in a vertical shift D units up / down • Ex: y = sin x + 1 shifts up 1 unit • Ex: y = cos x – 4 shifts down 4 units • Notice no parenthesis

  11. Combined Transformations • When working with multiple transformations, we want to rewrite the functions • This helps you see the phase shift

  12. How to graph • 1) determine the period, amplitude, and shifts • 2) graph and shift the period, and split it into 4 regions • 3) plot a point in between each region, including the amplitude and shifts in your calculations • 4) connect the points in the correct sine or cosine wave

  13. Ex • Sketch a graph of

  14. Ex • Sketch a graph of

  15. Closure • Graph • HW: p.523 #1-25 odds

  16. 5.6 Transformations of Sine and Cosine cont’dTues Feb 4 • Do Now • Graph the following • 1) y = sin(1/2 x)] • 2) y = - 2cos( 2x )

  17. HW Review: p.523 #1-25 odds

  18. Review of Sine and Cosine • Recall the transformations • A affects the amplitude • B affects the period • C/B affects the phase shift • D affects the vertical shift

  19. Ex • Graph

  20. Matching • On p.522

  21. Closure • What kind of transformations can affect the sine and cosine graphs? How do we determine what transformations occur? • HW: p.523 #27-43 odds

  22. 5.6 Addition and Multiplication of OrdinatesWed Feb 5 • Do Now • Graph

  23. HW Review: p.523 #27-43

  24. Graphs of Sums: Additions of Ordinates • When graphing a sum of 2 trigonometric functions, we use a strategy called addition of ordinates

  25. Properties of sums • The period of a sum will be the least common multiple of every period • Graph each important point by adding the y-values of each trig function

  26. ex • Graph y = 2sin x + sin 2x

  27. Damped Oscillation: Multiplication of Ordinates • We’ll just graph these

  28. Finding zeros (review) • To find zeros of a function, • 1) Graph function • 2) 2nd -> calc -> zeros • 3) Left bound – pick a point slightly left of the zero you want • 4) Right bound – pick a point slight right of the zero you want • 5) Guess – hit enter

  29. ex • Solve the zeros of on the interval [-12,12]

  30. closure • What is addition of ordinates? How do we graph these functions? • HW: p.524 #45-73 odds

  31. 5.6 Other Trig TransformationsThurs Feb 6 • Do Now • Graph y = csc x and y = tan x on your calculator

  32. HW Review: p.524 #45-73 odds

  33. Review: f(x) = tan x and cot x • The period of tangent and cotangent is pi • Each period is separated by vertical asymptotes • Amplitude does not affect the graph drastically

  34. Basic graphs • Y = tan x y = cot x

  35. Review: f(x) = csc x and sec x • The period of csc x and sec x is 2pi • Vertical asymptotes occur every half period • The amplitude represents how close to the center each curve gets

  36. Basic Graphs • Y = csc x y = sec x

  37. Transformations • Transformations affect these 4 graphs the same way

  38. Ex • Sketch the graph of

  39. Ex • Sketch the graph of

  40. Closure • Graph • HW: p. 525 #89-97 odds • CH 5 Test Wed and Thurs 02/12 and 02/13

  41. 5.6 ReviewFri Feb 7 • Do Now • Sketch the graph of

  42. HW Review p.525 #89-97

  43. Transformations Review • Basic graphs • Transformations • Period, Amplitude, Phase shift, Vertical shift

  44. Closure • What are some identifying properties of trigonometric functions and their graphs? • SGO Assessment Wed Feb 12 • Ch 5 Test Thurs Feb 13

More Related