Quantitative Aptitude Important Formulas

Height & Distance - Important Formulas,Tricks and Examples

In a right.angled DOAB, where ÐBOA = q,

i)sin q = Perpendicular/Hypotenuse = AB/OB;

ii)cos q = Base/Hypotenuse = OA/OB;

iii)tan q = Perpendicular/Base = AB/OA = sin q/cos q;

iv)cosec q = 1/sin q = OB/AB;

v)sec q = 1/cos q = OB/OA;

vi)cot q = 1/tan q = OA/AB = cos q/sin q.

Trigonometrical identities:

i)sin2q + cos2q = 1.

ii)1+tan2q = sec2q

iii)1+cot2q = cosec2q

Values of T-ratios:-

q

0°

30°

45°

60°

90°

Sin q

0

½

1/Ö2

Ö3/2

1

Cos q

1

Ö3/2

1/Ö2

½

0

Tan q

0

1/Ö3

1

Ö3

Not defined

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 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.

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