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Chapter 13: Trigonometry

Chapter 13: Trigonometry. A. Serra. A. Labelling Right Angled Triangles . (Easy Review). Class work: HYPotenuse , angle and OPPosite . Individual work: Example 1: Do it & check your answers. Exercise 13A: 1 Extra: 13A: 2. B. The trigonometric ratios. CLASS WORK

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Chapter 13: Trigonometry

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  1. Chapter 13:Trigonometry A. Serra

  2. A. Labelling Right Angled Triangles.(Easy Review) Class work: HYPotenuse, angle and OPPosite. Individual work: • Example 1: Do it & check your answers. • Exercise 13A: 1 • Extra: 13A: 2

  3. B. The trigonometric ratios. CLASS WORK Little investigation: trigonometric ratios being fixed for a given angle. Geogebra: Discovering SOH-CAH-TOA Using GDC to calculate trigonometric ratios given an angle and thus a side. Also given sides calculate angle. INDIVIDUAL WORK • Copy formulae in page 393 • Examples 2,3 and 4: Do them & check your answers. • Exercises 13B.1:1 ; 13B.2:2 ;13B.3:3 • Extra: Other exercises in 13B • Extra (1 positive can be awarded): Do investigation1 and present it to class next lesson. First come first serve (Publish new topic in google group).

  4. C. Using Trigonometry in Geometric Figures CLASS WORK Examples: Isosceles triangles, Chords and Tangents, Diagonals in rectangles and rhombus, etc. INDIVIDUAL WORK • Examples 7,8: Do them & check your answers. • Exercise 13C1:1(a,b,c), • Exercise 13C2:2; • Exercise 13C3:1,3,5, 7(difficult). • Extra: any other exercise in 13C

  5. D. Problem Solving using Trigonometry.(VIS = Very Important Section!) CLASS WORK Calculating heights and distances which are very difficult or impossible to measure (eg. 13D11 in page 406) INDIVIDUAL WORK • Examples 9 and 19: Do them & check your answers. • Exercise 13D: 1,5,9,13 • Extra: Exercise 13D: Even numbers

  6. E. 3-D Problem solving.(Not as important as previous. You can exchange exercises) CLASS WORK Did Pythagoras use 3-D googles? Example 13E.1.4 INDIVIDUAL WORK • Example 11,12,13,14: Do them & check your answers. • Exercises 13E1: 1,3,5 • Exercise 13E2:4 • Extra: 13E any other exercise.

  7. F. Areas of triangles CLASS WORK Area= ½ base X height = ½ absinC ! (need to remember it, proof not needed, just applications). Example 13F2 in page 413 INDIVIDUAL WORK • Example 15 (do & check) • Exercise 13F: 1,3,5 • Extra: Exercise 13F: 2,4.

  8. G. The cosine rule CLASS WORK Pythagoras when no right angle? Cosine rule! a^2=b^2+c^2-2bc cosA(it is in formulae booklet  ) (proof not needed, just applications when 3sides or 2sides and included angle given). Examples 13G2 in page 415 INDIVIDUAL WORK • Examples 16 and 17 (do & check) • Exercise 13G: 1,3,5 • Extra: Exercise 13G: 2,4.

  9. H. The sine rule CLASS WORK In section F we learned that Area= ½ absinC Other perspectives? Find out the Sine Rule. (Applications when 2 angles and one side or 2 sides and a non-included angle) (it is in formulae booklet  ) Examples 13H1:2 in page 417 INDIVIDUAL WORK • Examples 18 and 19 (do & check) • Exercise 13H1: 1 • Exercise 13H2: 2 • Extra: Other exercises in 13H.

  10. I. Using the Sine and Cosine rules. CLASS WORK Trial and error VS. Memory: Cosine rule: 3 sides, 2sides and included angle Sine rule: one side and two angles, two sides and a non included angle. Examples 13I:2 in page 420 INDIVIDUAL WORK • Examples 20 and 21 (do & check) • Exercise 13I: 1,5,9,13 • Exercise 13I: Even numbers.

  11. Review • INDIVIDUAL WORK • Review Set 13A. (Questions 1-11) • Extra: Review Set 13B and/or 13C • NEXT • Unit 18: Trigonometric Functions.

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