The document provides information on trigonometric ratios including: 1) It defines the six main trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) using coordinates on a unit circle. 2) It explains the signs of the ratios in the four quadrants of the coordinate plane. 3) It discusses the range of values that the six ratios can take. 4) It provides a table of the exact ratio values for 0, π/6, π/4, π/3, π/2, π, 3π/2, and 2π. 5) It covers fundamental trigonometric

1. Trigonometric ratios
P (x,y)
(0,0)
Mind Flash
Study Quiz
map cards
Exit

2. Study section

3. Table of contents
M1-2.a : Understand trigonometric ratios for a standard unit circle
M1-2.b : Know signs of trigonometric ratios
M1-2.c : Understand range of trigonometric ratios
M1-2.d : Know ratios of standard angles
M1-2.e : Learn the Fundamental identities
M1-2.f : Understand relation between ratios of Ɵ and -Ɵ

4. M1-2.a : Understand trigonometric ratios for a
standard unit circle
Ratios 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)
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5. M1-2.b : Know signs of trigonometric ratios
o Different signs in different quadrants
Y axis
2nd quadrant 1st quadrant
(-,+) (+,+)
X axis
O
3rd quadrant 4th quadrant
(-,-) (+,-)
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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
+ - + -
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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
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8. M1-2.d : Know ratios of standard angles
A 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
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9. M1-2.e : Learn the Fundamental identities
From distance formula,
(x-0)2 + (y-0)2 = 1
x2+ y2 = 1
P (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
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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
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11. End of study section

12. Quiz section

13. Question 1
Calculate 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 1
Calculate 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 1
Calculate 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 1
Calculate 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 1
Calculate 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 1
Sin Ɵ = opposite/hypotenuse
Sin Ɵ = 12/AC
0.6 = 12/AC
AC =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 =________
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26. Flash card 1
s
r
Ɵ
O
Length of arcarc = s = r Ɵ
Length of = s =________
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27. Flash card 1
s
r
Ɵ
O
Length of arc = s = r Ɵ
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28. Flash card 2
Sector
Ɵ
O r
Area ofof a sector = ½ r2Ɵ
Area a sector = _______
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29. Flash card 2
Sector
Ɵ
O r
Area ofof a sector = ½ r2Ɵ
Area a sector = _______
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30. Flash card 2
Sector
Ɵ
O r
Area of a sector = ½ r2Ɵ
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31. Flash card 3
1ᶜ= (180/ Π) o
1ᶜ= ________ o
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32. Flash card 3
1ᶜ= (180/ Π) o
1ᶜ= ________ o
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33. Flash card 3
1ᶜ= (180/ Π) o
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34. Flash card 4
1o = (Π /180)ᶜ
1o = _______ᶜ
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35. Flash card 4
1o = (Π /180)ᶜ
1o = _______ᶜ
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36. Flash card 4
1o = (Π /180)ᶜ
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37. End of Flash card section