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