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# Trigonometric ratios

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### Transcript

• 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