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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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
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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
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