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# 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