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IMPORTANT FACTS AND FORMULAE
1.We already know that:
In a rt.angled
∆ ΟΑΒ,
where
∠
BOA =
θ,
i)sin
θ =
Perpendicular/Hypotenuse = AB/OB;
ii)cos
θ = Β
ase/Hypotenuse = OA/OB;
iii)tan
θ =
Perpendicular/Base = AB/OA;
iv)cosec
θ = 1/
sin
θ = ΟΒ/ΑΒ;
v)sec
θ = 1/
cos
θ =
OB/OA;
vi)cot
θ = 1/
tan
θ =
OA/AB.
2.
Trigonometrical identities:
i)sin
2
θ
+ cos
2
θ = 1.
ii)1+tan
2
θ =
sec
2
θ
iii)1+cot
2
θ =
cosec
2
θ
3.
Values of Tratios:
θ
0
30
°
45
°
60
°
90
°
Sin
θ
0
½
1/
√2
√3/2
1
Cos
θ
1
√3/2
1/
√2
½
0
Tan
θ
0
1/
√3
1
√3
Not defined
4.
Angle of Elevation:
Suppose a man from a point O looks up an object P, placed above
the level of his eye. Then, the angle which the line of sight makes with the horizontal
through O, is called the angle of elevation of P as seen from O.
∴
Angle of elevation of P from O =
∠
AOP.
5.
Angle of Depression
: Suppose a man from a point O looks down at an object P, placed
below the level of his eye, then the angle which the line of sight makes with the
horizontal through O, is called the angle of depression of P as seen from O.
hypotenuse
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 Spring '11
 vinh

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