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Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
Trigonometric ratios
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Trigonometric ratios

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  • 1. Trigonometric ratios P (x,y) (0,0) Mind FlashStudy Quiz map cards Exit
  • 2. Study section
  • 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. 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. 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. 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. 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. 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. 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. 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. End of study section
  • 12. Quiz section
  • 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. 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. 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. 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. 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. Explanation to Question 1Sin Ɵ = opposite/hypotenuseSin Ɵ = 12/AC0.6 = 12/ACAC =20 cm Next
  • 19. End of quiz section
  • 20. Mind map section
  • 21. Trigonometric ratios Next
  • 22. Ratios of standard angles Next
  • 23. End of Mind map section
  • 24. Flash card section
  • 25. Flash card 1 s r Ɵ O Length of arcarc = s = r Ɵ Length of = s =________ See back Next
  • 26. Flash card 1 s r Ɵ O Length of arcarc = s = r Ɵ Length of = s =________ See back Next
  • 27. Flash card 1 s r Ɵ O Length of arc = s = r Ɵ See back Next
  • 28. Flash card 2 Sector Ɵ O r Area ofof a sector = ½ r2Ɵ Area a sector = _______ See back Prev Next
  • 29. Flash card 2 Sector Ɵ O r Area ofof a sector = ½ r2Ɵ Area a sector = _______ See back Prev Next
  • 30. Flash card 2 Sector Ɵ O r Area of a sector = ½ r2Ɵ See back Prev Next
  • 31. Flash card 3 1ᶜ= (180/ Π) o 1ᶜ= ________ o See back Prev Next
  • 32. Flash card 3 1ᶜ= (180/ Π) o 1ᶜ= ________ o See back Prev Next
  • 33. Flash card 3 1ᶜ= (180/ Π) o See back Prev Next
  • 34. Flash card 4 1o = (Π /180)ᶜ 1o = _______ᶜ See back Prev Next
  • 35. Flash card 4 1o = (Π /180)ᶜ 1o = _______ᶜ See back Prev Next
  • 36. Flash card 4 1o = (Π /180)ᶜ See back Prev Next
  • 37. End of Flash card section

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