1 / 22

Graphs of Sine and Cosine

Graphs of Sine and Cosine. Section 4.5. Sine Curve. 1. π. 2π. -1. Key Points:. 0. π. 2π. Value:. 1. 0. -1. 0. 0. Cosine Curve. 1. π. 2π. -1. Key Points:. 0. π. 2π. Value:. 0. -1. 1. 1. 0. Equations. For the rest of this section, we will be graphing:

inara
Download Presentation

Graphs of Sine and Cosine

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. Graphs of Sine and Cosine Section 4.5

  2. Sine Curve 1 π 2π -1 Key Points: 0 π 2π Value: 1 0 -1 0 0

  3. Cosine Curve 1 π 2π -1 Key Points: 0 π 2π Value: 0 -1 1 1 0

  4. Equations • For the rest of this section, we will be graphing: y = a Sin (bx – c) + d y = a Cos (bx – c) + d y = Sin x a = 1 c = 0 b = 1 d = 0

  5. Graph the equation y = 2 Sin x 2 1 π 2π -1 -2 Key Points: 0 π 2π Value: 2 0 -2 0 0

  6. Amplitude (a) • Half the distance between the maximum and minimum values of the function • Given by the value of │a │ • Graph the functions: y = 4 Sin x y = ½ Cos x y = -2 Sin x

  7. y = 4 Sin x y = ½Cos x 4 y = -2Sin x 3 2 1 π 2π -1 -2 -3 -4

  8. y = a Sin (bx – c) + d b gives us the period of the curve Period = y = 4 Sin 2x 4 Amplitude = Period = = π

  9. Key Points Would having a period of π change the key points of the curve? 1 π 2π -1

  10. Finding Key Points In General For Y = 4Sin 2x Find the period of the curve Divide the period into 4 equal parts From your starting point, add this distance 4 times for each period Period = π Distance = 0, , , ,

  11. y = 4Sin 2x 4 1 π -1 -4

  12. Graph the following curves • y = 4 Cos 8x • y = ½ Cos 2πx • y = -2 Sin 6x

  13. y = 4Cos 8x Amplitude = 4 b = 8 → Period = → Distance = 4 -4

  14. y = ½Cos 2πx Amplitude = ½ b = 2π → Period = → Distance = ½ - ½

  15. y = -2Sin 6x Amplitude = 2 b = 6 → Period = → Distance = 2 - 2

  16. y = a Sin (bx – c) + d • a = • b = • c = amplitude Find the period → Find the “phase shift” → horizontal shift →

  17. y = ½ Sin (x - ) • a = • b = • c = ½ 1 → Period = → P. S. =

  18. y = -3 Cos (2πx + 4π) • a = • b = • c = 3 2π → Period = → P. S. =

  19. y = a Sin (bx – c) + d • a = • b = • c = • d = amplitude Find the period → Find the “phase shift” → Vertical Shift

  20. y = • a = • b = • c = • d = 2 → Period = → P. S. = 3

  21. y = • a = • b = • c = • d = 4 → Period = → P. S. = -2

  22. y = 2 1 4 -2 -2 -6

More Related