Trigonometric Ratios
In a right angle triangle ABC where C = 900
We can define following term for angle A.
Base/Adjacent: Side adjacent to angle
Perpendicular/Opposite: Side opposite to right angle
Hypotenuse: Side opposite to right angle.
We can define the trigonometric ratios for angle A as
sin A = Perpendicular/Hypotenuse = BC/AB
cosec A = Hypotenuse/Perpendicular = AB/BC
cos A = Base/Hypotenuse = AC/AB
sec A = Hypotenuse/Base = AB/AC
tan A = Perpendicular/Base = AB/AC
cot A = Base/Perpendicular = AC/AB
Reciprocal of functions:
The reciprocal of sin A is cosec A
sin A = 1/cosec A
The reciprocal of cos A is sec A
cos A = 1/sec A
The reciprocal of tan A is cot A
tan A = 1/cot A
These are valid for acute angles
We can define tan A = sin A/cos A
cot A = cos A/sin A
Value of sin and cos is always less than 1
Trigonometric Ratios of complimentary angles:
sin (90 – A) = cos A
cos (90 – A) = sin A
tan (90 – A) = cot A
cot (90 – A) = tan A
sec (90 – A) = cosec A
cosec (90 – A) = sec A
Trigonometric Identities
sin2 A + cos 2A = 1
1 + tan2 A = sec2 A
1 + cot2 A = cosec2 A
Trigonometric Ratios of common angles:
Double Angle Formulas:
sin 2A = 2 sin A cos A = [2 tan A/(1 + tan2 A)]
cos 2A = cos2 A – sin2 A = 1 – 2 sin2 A = 2 cos2 A – 1 = [(1 – tan2 A)/ [(1 – tan2 A)]
tan 2A = 2 tan A/ (1 – tan2 A)
Triple Angle Formulas:
sin 3A = 3 sin A – 4 sin3 A
cos 3A = 4 cos3 A – 3 cos A
tan 3A = [3 tan A – tan3 A]/ [1 – 3 tan2 A]