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11 X1 T04 01 trigonometric ratios (2010)

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11 X1 T04 01 trigonometric ratios (2010)

  1. 1. Trigonometric Ratios
  2. 2. Trigonometric Ratios  hypotenuse adjacent opposite
  3. 3. Trigonometric Ratios opp sin    hypotenuse hyp adjacent adj cos   hyp opp opposite tan   adj
  4. 4. Trigonometric Ratios hyp opp sin   cosec   hypotenuse hyp opp adjacent adj hyp cos   sec  hyp adj opp adj opposite tan   cot   adj opp
  5. 5. Trigonometric Ratios hyp opp sin   cosec   hypotenuse hyp opp adjacent adj hyp cos   sec  hyp adj opp adj opposite tan   cot   adj opp e.g.  i  sin x  cos 25
  6. 6. Trigonometric Ratios hyp opp sin   cosec   hypotenuse hyp opp adjacent adj hyp cos   sec  hyp adj opp adj opposite tan   cot   adj opp e.g.  i  sin x  cos 25 x  90  25 x  65
  7. 7. Trigonometric Ratios hyp opp sin   cosec   hypotenuse hyp opp adjacent adj hyp cos   sec  hyp adj opp adj opposite tan   cot   adj opp e.g.  i  sin x  cos 25  ii  cot  x  20   tan  x  30  x  90  25 x  65
  8. 8. Trigonometric Ratios hyp opp sin   cosec   hypotenuse hyp opp adjacent adj hyp cos   sec  hyp adj opp adj opposite tan   cot   adj opp e.g.  i  sin x  cos 25  ii  cot  x  20   tan  x  30  x  90  25 x  20  x  30  90 x  65 2 x  80 x  40
  9. 9.  iii  a 61 13
  10. 10. a  iii   tan 61 13 a 61 13
  11. 11. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13
  12. 12. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  32 x 5
  13. 13. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  5  sin 32 x 32 x 5
  14. 14. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  5  sin 32 x 5 32 x x sin 32 x  9.4 units (to 1 dp) 5
  15. 15. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  5  sin 32 x 5 32 x x sin 32 x  9.4 units (to 1 dp) 5 v 14  10
  16. 16. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  5  sin 32 x 5 32 x x sin 32 x  9.4 units (to 1 dp) 5 10 v cos   14 14  10
  17. 17. a  iii   tan 61 13 a a  13tan 61 61 a  23.5 units (to 1 dp) 13  iv  5  sin 32 x 5 32 x x sin 32 x  9.4 units (to 1 dp) 5 10 v cos   14 14 10   cos 1 14    44 25 10
  18. 18. Exact Ratios 60 60 60
  19. 19. Exact Ratios 60 2 2 60 60 2
  20. 20. Exact Ratios 30 2 3 60 1
  21. 21. Exact Ratios 1 sin 30   2 30 2 3 3 cos30   2 60 tan 30   1 1 3
  22. 22. Exact Ratios 1 3 sin 30   sin 60  2 2 30 2 3 cos 60   1 3 cos30   2 2 60 tan 30   1 tan 60  3 1 3
  23. 23. Exact Ratios 1 3 sin 30   sin 60  2 2 30 2 3 cos 60   1 3 cos30   2 2 60 tan 30   1 tan 60  3 1 3 45 2 1 45 1
  24. 24. Exact Ratios 1 3 sin 30   sin 60  2 2 30 2 3 cos 60   1 3 cos30   2 2 60 tan 30   1 tan 60  3 1 3 1 sin 45  2 45 1 2 cos 45   1 2 45  tan 45  1 1
  25. 25. Alternative way of remembering the exact ratios 0 30 45 60 90 sin cos tan
  26. 26. Alternative way of remembering the exact ratios 0 30 45 60 90 0 1 2 3 4 sin 2 2 2 2 2 cos tan
  27. 27. Alternative way of remembering the exact ratios 0 30 45 60 90 0 1 2 3 4 sin 2 2 2 2 2 4 3 2 1 0 cos 2 2 2 2 2 tan
  28. 28. Alternative way of remembering the exact ratios 0 30 45 60 90 0 1 2 3 4 sin 2 2 2 2 2 4 3 2 1 0 cos 2 2 2 2 2 tan sin  cos
  29. 29. Alternative way of remembering the exact ratios 0 30 45 60 90 0 1 2 3 4 sin 2 2 2 2 2 4 3 2 1 0 cos 2 2 2 2 2 tan 0 1 2 3 4 sin  4 3 2 1 0 cos
  30. 30. Measuring Angles
  31. 31. Measuring Angles Angle of Elevation B  A
  32. 32. Measuring Angles Angle of Elevation B  A angle of elevation of B from A
  33. 33. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A
  34. 34. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A angle of depresion of X from Y
  35. 35. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A angle of depresion of X from Y Note: angle of elevation = angle of depression
  36. 36. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A angle of depresion of X from Y Note: angle of elevation = angle of depression Compass Bearings N W E S
  37. 37. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A angle of depresion of X from Y Note: angle of elevation = angle of depression Compass Bearings NW N NE W E SW S SE
  38. 38. Measuring Angles Angle of Elevation Angle of Depression B Y   A X angle of elevation of B from A angle of depresion of X from Y Note: angle of elevation = angle of depression Compass Bearings NW NNW N NE NNE WNW ENE W E WSW ESE SW SSW S SSE SE
  39. 39. True Bearings Always start NORTH and measure clockwise
  40. 40. True Bearings Always start NORTH and measure clockwise X Y
  41. 41. True Bearings Always start NORTH and measure clockwise X Y Bearing of Y from X
  42. 42. True Bearings Always start NORTH and measure clockwise N X 30 Y Bearing of Y from X
  43. 43. True Bearings Always start NORTH and measure clockwise N X 30 Y Bearing of Y from X 120 T or S60 E
  44. 44. True Bearings Always start NORTH and measure clockwise N X 30 Y Bearing of Y from X Bearing of X from Y 120 T or S60 E
  45. 45. True Bearings Always start NORTH and measure clockwise N X 30 N 60 Y Bearing of Y from X Bearing of X from Y 120 T or S60 E
  46. 46. True Bearings Always start NORTH and measure clockwise N X 30 N 60 Y Bearing of Y from X Bearing of X from Y 120 T 300 T or S60 E or N60 W
  47. 47. Exercise 4A; 1 to 3 (pick some), 4acf, 5, 7bd, 8ac, 9bd, 11, 12, 14c, 17, 18, 19b, 21, 23, 24, 25 Exercise 4B; 1b, 2b, 3, 4b, 6, 7, 10

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