12 x1 t03 01 arcs & sectors (2012)

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12 x1 t03 01 arcs & sectors (2012)

  1. 1. Trigonometric Functions
  2. 2. Trigonometric Functions 360  2 radians
  3. 3. Trigonometric Functions 360  2 radiansArcs & Sectors
  4. 4. Trigonometric Functions 360  2 radiansArcs & Sectors C  2r
  5. 5. Trigonometric Functions 360  2 radiansArcs & Sectors C  2r A  r 2
  6. 6. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2 O  B
  7. 7. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2 O  B AB is an arc
  8. 8. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2 O  l B AB is an arc
  9. 9. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2  l  2r O  l 2 B AB is an arc
  10. 10. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2  l  2r O  l 2 l  r B AB is an arc
  11. 11. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2  l  2r O  l 2 l  r B Length of an arc; l  r AB is an arc
  12. 12. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2  l  2r O  l 2 l  r B OAB is a sector Length of an arc; l  r AB is an arc
  13. 13. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2   l  2r AOAB   r 2 O  l 2 2 l  r B OAB is a sector Length of an arc; l  r AB is an arc
  14. 14. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2   l  2r AOAB   r 2 O  l 2 2 l  r 1 B AOAB  r 2 2 OAB is a sector Length of an arc; l  r AB is an arc
  15. 15. Trigonometric Functions 360  2 radiansArcs & Sectors A C  2r A  r 2   l  2r AOAB   r 2 O  l 2 2 l  r 1 B AOAB  r 2 2 OAB is a sector Length of an arc; l  r AB is an arc 1 2 Area of a sector; A  r  2
  16. 16. e.g. A m 5c 45 O B
  17. 17. e.g. A l AB  r m 5c 45 O B
  18. 18. e.g. A l AB  r    5  m 4 5c 45 O B
  19. 19. e.g. A l AB  r    5  m 4 5c 45 B 5 O  cm 4
  20. 20. e.g. 1 l AB  r AOAB  r 2 A 2    5  m 4 5c 45 B 5 O  cm 4
  21. 21. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 O  cm 4
  22. 22. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 25 O  cm  cm 2 4 8
  23. 23. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 25 O  cm  cm 2 4 8 Area minor segment AB 
  24. 24. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 25 O  cm  cm 2 4 8 1 1 Area minor segment AB  r 2  r 2 sin  2 2 1 2  r   sin   2
  25. 25. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 25 O  cm  cm 2 4 8 1 1 Area minor segment AB  r 2  r 2 sin  2 2 1 2  r   sin   2
  26. 26. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c 45 2 4 B 5 25 O  cm  cm 2 4 8 1 1 Area minor segment AB  r 2  r 2 sin  2 2 1 2  r   sin   2 1 2   5   sin  2 4 4 25   1      2 4 2 25 2  100 2  cm 8 2
  27. 27. e.g. 1 l AB  r AOAB  r 2 A 2   1 2   5   5   m 4   5c45 2 4 B 5 25 O  cm  cm 2 4 8 1 1 Area minor segment AB  r 2  r 2 sin  2 2 1 2  r   sin   2 1 2   5   sin  Exercise 14B; 2 to 24 evens, 25, 28* 2 4 4 25   1      2 4 2 25 2  100 2  cm 8 2

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