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Chapter 18: Trigonometric Functions

Chapter 18: Trigonometric Functions. A. Serra. A. Observing periodic Behaviour (Easy Review). Class work: Math experiment: Observing periodic behaviour in a Ferris wheel and ideas for project. Periodic function, the period p f( x+p )=f(x), amplitude, principal axis. Individual work:

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Chapter 18: Trigonometric Functions

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  1. Chapter 18:Trigonometric Functions A. Serra

  2. A. Observing periodic Behaviour(Easy Review) Class work: Math experiment: Observing periodic behaviourin a Ferris wheel and ideas for project. Periodic function, the period p f(x+p)=f(x), amplitude, principal axis. Individual work: • Example 1: Do it & check your answers. • Exercise 18A: 1,3 • Extra: 18A: 2,4

  3. B. The sine function. CLASS WORK The basic sine curve (recap on our Ferris Wheel experiment). Using GDC. Geogebra Experiment: Sine wave transformations. State period and amplitud: Investigation i: y=m sinx (vertical dilation) Investigation ii: y= sin kx (horizontal dilation) Investigation iii: y= sinx +b (vertical translation) Investigation iv: y= sin (x-a) (horizontal translation) INDIVIDUAL WORK • Copy the general sine function properties in page 567 • Examples 1,2 and 3: Do them & check your answers. • Exercises 18B.1:1 ; 18B.2:1 • Extra: Other exercises in 18B • Extra (1 positive can be awarded): Do investigation4 (page 568) and present it to class next lesson. First come first serve (Publish new topic in google group).

  4. C. The cosine function CLASS WORK Geogebra: Cosine function workshop. Investigation 4 (volunteers presentation) INDIVIDUAL WORK • Copy conclusions from investigation 4 (see blue box in page 569) • Example 4: Do them & check your answers. • Exercise 18C: 1,4 • Extra: Exercise 18C: 2,3

  5. D. Modelling using sine and cosine functions CLASS WORK Example in page 570 and ideas for project. INDIVIDUAL WORK • Examples 9 and 19: Do them & check your answers. • Exercise 18D: 1,2 • Extra: Exercise 18D: 3,4

  6. E. Trigonometric equations CLASS WORK Using graphs (eg y=cosx, page 573) and GDC to solve trigonometric equations (egcosx=0.5) INDIVIDUAL WORK • Example 5: Do it & check your answers. • Exercises 18E1: 1,3,5 (do them with and without GDC) • Extra: 18E any other exercise.

  7. F. Using trigonometric models CLASS WORK Example 18F2 in page 576 INDIVIDUAL WORK • Example 6(do & check) • Exercise 18F: 1,3 • Extra: Exercise 18F: 2,4.

  8. Review • INDIVIDUAL WORK • Review Set 18A. (Questions 1-11) • Extra: Review Set 18B and/or 18C • NEXT • Units 13 and 18: mock test • Units 13& 18: Test • Good luck 

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