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Trigonometric graphs

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  1. Trigonometric graphs

  2. Don’t forget to label the axes! y 1 x 0o 90o 180o 360o 270o -1 Graph of Sine • y = sin x Plot the ‘special’ points!

  3. General Form: y = asin(bx)+c • a affects the amplitude • b affects the frequency (no. of cycles) • c shifts the graph up/down

  4. 0o 90o 180o 360o 270o Exercise 1: y = sin(x) + 3 y 4 3 2 1 x -1

  5. 0o 90o 180o 360o 270o Exercise 1: y = sin(x) − 2 y 1 x − 1 −2 −3

  6. 0o 90o 180o 360o 270o Effect of ‘a’ y 2 • y = sin x and y = 2sin x 1 x −1 −2

  7. y 1 x 0o 90o 180o 360o 270o -1 Effect of ‘b’ • y = sin x and y = sin2x

  8. y 1 x 0o 90o 180o 360o 270o -1 Effect of Modulus • y = sin x and y = |sin x|

  9. Don’t forget to label the axes! y 1 x 0o 90o 180o 360o 270o -1 Graph of Cosine • y = cos x Plot the ‘special’ points!

  10. Don’t forget to label the axes! y 1 x 0o 90o 180o 360o 270o -1 Graph of Tangent Draw the asymptotes! • y = tan x Plot the ‘special’ points! Notice that the points at y = 1 are plotted in the middle of the two angles around them!

  11. Know that the amplitude is 2! Know that the graph is translated by 1 unit downwards! Don’t forget to label the axes! y 2 x 0o 90o 180o 360o 270o -2 Draw the reference line y = -1 Example: y = 2cos x – 1 Plot the ‘special’ points! This is the graph of y = 2cos x

  12. y 2 x 0o 90o 180o 360o 270o -2 Example: y = 2cos x – 1 1 -3

  13. Know that the graph is stretched by factor 3 along the y axis! Know that the graph is translated by 6 units downwards! Don’t forget to label the axes! y 3 x 0o 90o 180o 360o 270o -3 Notice that the reference points are now 3 and -3! Example: y = 3tan x – 6 Draw the asymptotes! Plot the ‘special’ points! Notice that the points at y = 1 are plotted in the middle of the two angles around them!

  14. y 3 x 0o 90o 180o 360o 270o -3 -9 Draw the reference line y = -6 Example: y = 3tan x – 6

  15. y 3 0o 90o 180o 360o 270o -3 Example: y = 3tan x – 6 x -9

  16. y 3 0o 90o 180o 360o 270o -3 Example: y = 3tan x – 6 x -9

  17. Don’t forget to label the axes! y 2 x 0o 90o 180o 360o 270o -2 Plotting two graphs on the same axes • y = 2sin x and y = cos x Plot the ‘special’ points!

  18. y 2 x 0o 90o 180o 360o 270o -2 Plotting two graphs on the same axes • y = 2sin x and y = cos x This is the graph of y = 2sinx

  19. y 2 1 x 0o 90o 180o 360o 270o -1 -2 Plotting two graphs on the same axes • y = 2sin x and y = cos x

  20. Label the two graphs! y 2 1 x 0o 90o 180o 360o 270o -1 -2 Plotting two graphs on the same axes • y = 2sin x and y = cos x y = 2sinx y = cosx