1. Trigonometry θ W=weight of the van Force F= W x Sinθ Work = F · S
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W=weight of the van
Force F= W x Sinθ
Work = F · S θ F
Trigonometry w θ
Wave Motion
x = kt
y= asint
P(x,y)
P(x,y) 2b 2a
Orbit of Planet
x = acos, y= bsin)

2. Definition of sin ratio
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Definition of sin ratio ϴ r
P(x,y)

3. Range of sin ratio is [-1,1]
B(0,r) r r
B(0,-r)
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4. Graph of sin ratio 1
90
180
270
360 -1
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5. Application of sin ratioθ A B C D h c b a
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6. Sine Rule A B C D h c b a
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7. Definition of cosine ratioϴ r
P(x,y)
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8. Simple Harmonic Motion
P(x,y)
Orbit of Planet
x = acos, y= bsin) 2b 2a
P(x,y)
Simple Harmonic Motion
x = acos, y = 0 2a
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9. θ Wave Motion x = kt y= asint W=weight of the van Force F= W x Sinθ
P(x,y) s
W=weight of the van
Force F= W x Sinθ
Work = F x S θ F w θ
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10. Range of cos ratio is [-1,1]
A(r,0)
A(-r,0)
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11. Graph of cos ratio 1
Cos θ 
90
180
270
360
θ  -1
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12. Application of sin & cosine ratios Parametric equation of circle isϴ r
P(rcosθ, rsin θ)
Parametric equation of circle is
x = r.cos(θ) & y = r.sin(θ)
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13. Definition of tan ratio
P(x,y) r ϴ
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14. Application of tan ratio
650
h = ?
50m
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15. Definition of cosec ratio
P(x,y) r ϴ
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16. Definition of sec ratioϴ r
P(x,y)
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17. Definition of cot ratio
P(x,y) r ϴ
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18. In the second quadrant sin & cosec ratios are positive
In the first quadrant all ratios are positive
(+,+)
(-,+)
(-,-)
(+,-)
In the third quadrant tan & cot ratios are positive
In the fourth quadrant cosine & sec ratios are positive
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19. Two out six trigonometric ratios of quadrantal angles are not defined
As y = 0, cot & cosec ratios are not defined.
tan 1800 = sec 1800 = 0
As x = 0, tan & sec ratios are not defined.
cot 900 = cosec 900 = 0
(0,+)
(+,0)
(-,0)
(0,-)
As x = 0, tan & sec ratios are not defined.
cot 2700 = cosec 2700 = 0
As y = 0, cot & cosec ratios are not defined.
tan 00 = sec 00 = 0
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20. BAPAT CLASSES®

21. BAPAT CLASSES®

22. As cot θ = cos θ / sin θ cos θ = cot θ x sin θ By invertendo
sec θ = tan θ x cosec θ
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23. If tan θ  0 & cot θ  0 then Cot θ = 1/ tan θ i.e. tan θ x cot θ = 1
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24. BAPAT CLASSES®

25. BAPAT CLASSES®

26. A B C
30
90 1 2
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27. A B C
60
90 1 2
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28. A B C
45
90 1
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29. A
B(0,r)
90 r
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30. BAPAT CLASSES® A r .
B(r,0)

31. A
B(x,y)
+θ
-θ
B’(x,-y) C r
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32. B(x,y) r
+θ A C
-θ r
B’(x,-y)
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33. sin(-θ) = -sin(θ) cos(-θ) = cos(θ) tan(-θ) = -tan(θ)
cosec(-θ) = -cosec(θ)
sec(-θ) = sec(θ)
cot(-θ) = -cot(θ)
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34. sin(-30) = -sin(30) = 0.500 cos(-45) = cos(45) = 0.707
tan(-45) = -tan(45) = -1
cosec(-90) = -cosec(90) = -1
sec(-60) = sec(60) = 2
cot(-30) = -cot(30) =
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35. Trigonometric Ratios of Complementary angles
90-x
cos x = sin (90-x)
sin x = cos (90-x) 90 x
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36. Trigonometric Ratios of Complementary angles
90-x
cosec x = sec (90-x)
sec x = cosec (90-x) x 90
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37. Trigonometric Ratios of Complementary angles
90-x
cot x = tan (90-x)
tan x = cot (90-x) 90 x
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38. If cos A = sin B then A + B = 90 If cos A = sin 50 then A = 40
If cot A = tan B then A + B = 90
If cot 20 = tan B then B = 70
If cosec A = sec B then A + B = 90
If cosec A = sec 25 then A = 65
Trigonometric Ratios of Complementary angles
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39. If angles A and B are in the same quadrant then
cos A = cos B  A = B
sin A = sin B  A = B
tan A = tan B  A = B
If cos A = cos 50 then A = 50
If sin 20 = sin B then B = 20
If tan A = tan 45 then A = 45
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40. If angles A and B are in the If cosec A = cosec 50 then A = 50
same quadrant then
cosec A = cosec B  A = B
sec A = sec B  A = B
cot A = cot B  A = B
If cosec A = cosec 50 then A = 50
If sec 20 = sec B then B = 20
If cot A = cot 45 then A = 45
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41. Trigonometric Identities
sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = cosec2x
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42. Trigonometric Identities
As sin2x + cos2x = 1
sin2x = 1- cos2x
cos2x = 1-sin2x
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43. Application of Trigonometric Identity
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44. Application of Trigono
metric Identities
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45. Application of Trigonometric Identities
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46. Trigonometric Identities
As 1+ tan2x = sec2x
Sec2x - tan2x = 1
tan2x = sec2x - 1
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47. Application of Trigonometric Identities
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48. Trigonometric Identities
As 1+ cot2x = cosec2x
cosec2x - cot2x = 1
cot2x = cosec2x - 1
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49. (1+sinx)(1-sinx) = 1 - sin2x (1+sinx)(1-sinx) = cos2x
Identities
As (a + b)(a - b) = a2 – b2
(1+sinx)(1-sinx) = 1 - sin2x
(1+sinx)(1-sinx) = cos2x
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50. Identities As a3 – b3 =(a - b)3 +3ab(a-b)
sec6x -tan6x=(sec2 x-tan2 x)3
+ 3sec2xtan2x(sec2x-tan2x)
sec6x -tan6x =1+3sec2xtan2x
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51. BAPAT CLASSES®

52. x = acos
y = bsin
Eliminate 
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