Trigonometric ratios

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Trigonometric ratios

  1. 1. Trigonometric ratios P (x,y) (0,0) Mind FlashStudy Quiz map cards Exit
  2. 2. Study section
  3. 3. Table of contentsM1-2.a : Understand trigonometric ratios for a standard unit circleM1-2.b : Know signs of trigonometric ratiosM1-2.c : Understand range of trigonometric ratiosM1-2.d : Know ratios of standard anglesM1-2.e : Learn the Fundamental identitiesM1-2.f : Understand relation between ratios of Ɵ and -Ɵ
  4. 4. M1-2.a : Understand trigonometric ratios for a standard unit circleRatios are defined as co-ordinates of a point on a standard unit circle B (0,1) Sine Ɵ = sin Ɵ = y P (x,y) Cosine Ɵ = cos Ɵ = x sin Ɵ Tangent Ɵ = tan Ɵ = = C (-1,0) Ɵ A (1,0) cos Ɵ 1 1 O (0,0) Cosecant Ɵ = cosec Ɵ = sin Ɵ = 1 1 Secant Ɵ = sec Ɵ = = cos Ɵ cos Ɵ Cotangent Ɵ = cot Ɵ = sin Ɵ = D (0,-1) P (x,y) = P (cos Ɵ,sin Ɵ) Back to Index Prev Next
  5. 5. M1-2.b : Know signs of trigonometric ratioso Different signs in different quadrants Y axis 2nd quadrant 1st quadrant (-,+) (+,+) X axis O 3rd quadrant 4th quadrant (-,-) (+,-) Back to Index Prev Next
  6. 6. M1-2.b : Know signs of trigonometric ratios (-,+) (+,+) (-,-) (+,-)Quadrant/Ratio 1st 2nd 3rd 4th Sin x + + - - Cos x + - - + Tan x + - + - Cosec x + + - - Sec x + - - + Cot x + - + - Back to Index Prev Next
  7. 7. M1-2.c : Understand range of trigonometric ratios (0,1) We observe that – 1 ≤ sin x ≤ 1 and – 1 ≤ cos x ≤ 1(-1,0) (1,0) (0,0) Since cosec x = (1/sin x) cosec x = -1 or = 1 Also, since sec x = (1/cos x) (0,-1) sec x =-1 or =1 tan x and cot x can take any real value Back to Index Prev Next
  8. 8. M1-2.d : Know ratios of standard anglesA ngle/ Ratio 0 π/ 6 π/ 4 π/ 3 π/ 2 π 3π/ 2 2π S in x 0 1/2 1/ 2 3/2 1 0 -1 0 C os x 1 3/2 1/ 2 1/2 0 -1 0 1 T an x 0 1/ 3 1 3 Not 0 Not 0 defined defined Back to Index Prev Next
  9. 9. M1-2.e : Learn the Fundamental identities From distance formula, (x-0)2 + (y-0)2 = 1 x2+ y2 = 1P (x,y) Thus, sin2 Ɵ + cos2 Ɵ = 1 (0,0) Dividing by cos2 Ɵ tan2 Ɵ + 1 = sec2 Ɵ Dividing by sin2 Ɵ 1+ cot2 Ɵ = cosec2 Ɵ Back to Index Prev Next
  10. 10. M1-2.f : Understand relation between ratios of Ɵ and -Ɵ For point P, sin Ɵ = y and cos Ɵ = x P (x,y) For point Q Ɵ sin (-Ɵ) = -y and cos (-Ɵ) = O (0,0) -Ɵ A (1,0) x Comparing the two, Q (x,-y) y = sin Ɵ = - sin (-Ɵ) i.e. sin (-Ɵ) = - sin Ɵ And x = cos Ɵ = cos (-Ɵ) i.e. cos (-Ɵ) = cos Ɵ Back to Index Prev Next
  11. 11. End of study section
  12. 12. Quiz section
  13. 13. Question 1Calculate the length of the side AC, given that sin θ = 0.6 A Ɵ B 12 cm C 12 cm 16 cm 20 cm 8 cm Next
  14. 14. Question 1Calculate the length of the side AC, given that sin θ = 0.6 A Ɵ B 12 cm C 12 cm 16 cm 20 cm 8 cm That is correct! Explanation Next Q
  15. 15. Question 1Calculate the length of the side AC, given that sin θ = 0.6 A Ɵ B 12 cm C 12 cm 16 cm 20 cm 8 cm Next Q
  16. 16. Question 1Calculate the length of the side AC, given that sin θ = 0.6 A Ɵ B 12 cm C 12 cm 16 cm 20 cm 8 cm That is wrong, please try again… Explanation Next Q
  17. 17. Question 1Calculate the length of the side AC, given that sin θ = 0.6 A Ɵ B 12 cm C 12 cm 16 cm 20 cm 8 cm That is wrong, please try again… Explanation Next Q
  18. 18. Explanation to Question 1Sin Ɵ = opposite/hypotenuseSin Ɵ = 12/AC0.6 = 12/ACAC =20 cm Next
  19. 19. End of quiz section
  20. 20. Mind map section
  21. 21. Trigonometric ratios Next
  22. 22. Ratios of standard angles Next
  23. 23. End of Mind map section
  24. 24. Flash card section
  25. 25. Flash card 1 s r Ɵ O Length of arcarc = s = r Ɵ Length of = s =________ See back Next
  26. 26. Flash card 1 s r Ɵ O Length of arcarc = s = r Ɵ Length of = s =________ See back Next
  27. 27. Flash card 1 s r Ɵ O Length of arc = s = r Ɵ See back Next
  28. 28. Flash card 2 Sector Ɵ O r Area ofof a sector = ½ r2Ɵ Area a sector = _______ See back Prev Next
  29. 29. Flash card 2 Sector Ɵ O r Area ofof a sector = ½ r2Ɵ Area a sector = _______ See back Prev Next
  30. 30. Flash card 2 Sector Ɵ O r Area of a sector = ½ r2Ɵ See back Prev Next
  31. 31. Flash card 3 1ᶜ= (180/ Π) o 1ᶜ= ________ o See back Prev Next
  32. 32. Flash card 3 1ᶜ= (180/ Π) o 1ᶜ= ________ o See back Prev Next
  33. 33. Flash card 3 1ᶜ= (180/ Π) o See back Prev Next
  34. 34. Flash card 4 1o = (Π /180)ᶜ 1o = _______ᶜ See back Prev Next
  35. 35. Flash card 4 1o = (Π /180)ᶜ 1o = _______ᶜ See back Prev Next
  36. 36. Flash card 4 1o = (Π /180)ᶜ See back Prev Next
  37. 37. End of Flash card section

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