Download - Trigno Metry Fundas
In a right-angled triangle,
Sinθ= Opposite Side/Hypotenuse
Cosθ= Adjacent Side/Hypotenuse
Tanθ= Sinθ/Cosθ = Opposite Side/Adjacent Side
Cosecθ = 1/Sinθ= Hypotenuse/Opposite Side
Secθ = 1/Cosθ = Hypotenuse/Adjacent Side
Cotθ = 1/tanθ = Cosθ/Sinθ = Adjacent Side/Opposite Side
SinθCosecθ = CosθSecθ = TanθCotθ = 1
Sin(90-θ) = Cosθ, Cos(90-θ) = Sinθ
Sin²θ + Cos²θ = 1
Tan²θ + 1 = Sec²θ
Cot²θ + 1 = Cosec²θ
Addition and subtraction formula:-
Sin(A+B) = SinACosB + CosASinBSin(A-B) = SinACosb - CosASinBCos(A+B) = CosACosB - SinASinBCos(A-B) = CosACosB + SinASinB
Tan(A+B) = (TanA+TanB)/(1-TanATanB)
Tan(A-B) = (TanA - TanB)/(1+TanATanB)
Cot (A+B) = (CotACotB-1)/(CotA + CotB)
Cot(A-B) = (CotACotB+1)/(CotB-CotA)
Sin(A+B)+Sin(A-B) = 2SinACosB
Sin(A+B)-Sin(A-B) = 2CosASinB
Cos(A+B)+Cos(A-B) = 2CosACosB
Cos(A-B) - Cos(A-B) = 2SinASinB
SinC + SinD = 2Sin[(C+D)/2]Cos[(C-D)/2]
SinC - SinD = 2Cos[(C+D)/2]Sin[(C-D)/2]
CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2]
CosC - CosD = 2Sin[(C+D)/2]Sin[(D-C)/2]
Sin2θ = 2SinθCosθ = (2tanθ)/(1+tan²θ)
Cos2θ = Cos²θ - Sin²θ = 2Cos²θ - 1= 1 - 2Sin²θ = (1-tan²θ)/(1+tan²θ)
Tan2θ = 2tan²θ/(1-tanθ)
(Angles are given in degrees, 90 degrees, 180 degrees etc.)
I. Sin(-θ)=-SinθCos(-θ) = Cosθtan(-θ) = -tanθcot(-θ) = -cotθsec(-θ) = secθcosec(-θ)= - cosecθ
II.sin(90-θ) = cosθcos(90-θ) = sinθtan(90-θ) = cotθcot(90-θ) = tanθsec(90-θ) = cosecθcosec(90-θ) = secθ
III.sin(90+θ) = cosθcos(90+θ) = -sinθtan(90+θ) = -cotθcot(90+θ) = -tanθsec(90+θ) = -cosecθcosec(90+θ) = secθ
IV.sin(180-θ) = sinθcos(180-θ) = -cosθtan(180-θ) = -tanθ
cot(180-θ) = cotθsec(180-θ) = -secθcosec(180-θ) = cosecθ
V.sin(180+θ) = -sinθcos(180+θ) = -cosθtan(180+θ) = tanθcot(180+θ) = cotθsec(180+θ) = -secθcosec(180+θ) = -cosecθ
Formulas which express the sum or difference in product
Formulae which express products as sums or difference of Sines and Cosines
Trignometric ratios of Multiple Angles
Trignometric ratios of 3θ
Trignometric ratios of sub-multiple angles
Properties of Inverse Trignometric Functions
Properties of Triangles
Sine Formula (or Law of Sines)
In any ΔABC,
Cosine Formula (or Law of Cosines)
In any ΔABC,
These formulas are also written as
Projection formulas
In any ΔABC,
Half-Angles and Sides
In any ΔABC,
Area of a Triangle
Hero's fromula
Incircle and Circumcircle
A circle which touches the three sides of a traingle internally is called the incircle.The center of the circle is called the incentre and the raidus is called the inradius.
If r is the inradius, then
The circle which passes through the vertices of a triangle is called the circumcircle of a triangle or circumscribing circle. The centre of this circle is the circumcentre and the radius of the circumcircle is the circumradius.
If R is the circumradius, then
If Δ is the area of the triangle,
Hyperbolic Functions
Relation between circular and hyperbolic functions
Addition formulas for Hyperbolic functions
Periods of hyperbolic functions
Inverse Hyperbolic functions