Trigonometric Formulas

Posted By on December 21, 2014


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Logarithm Formulas
Hyperbolic Formulas

Right-Triangle Definitions

Right-Triangle Definition
sinα=OppositeHypotenuse
cosα=AdjacentHypotenuse
tanα=OppositeAdjacent
cscα=1sinα=HypotenuseOpposite
secα=1cosα=HypotenuseAdjacent
cotα=1tanα=AdjacentOpposite

Reduction Formulas

sin(x)=sin(x)
cos(x)=cos(x)
sin(π2x)=cos(x)
cos(π2x)=sin(x)
sin(π2+x)=cos(x)
cos(π2+x)=sin(x)
sin(πx)=sin(x)
cos(πx)=cos(x)
sin(π+x)=sin(x)
cos(π+x)=cos(x)

Basic Identities

sin2x+cos2x=1
tan2x+1=1cos2x
cot2x+1=1sin2x

Sum and Difference Formulas

sin(α+β)=sinαcosβ+sinβcosα
sin(αβ)=sinαcosβsinβcosα
cos(α+β)=cosαcosβsinαcosβ
cos(αβ)=cosαcosβ+sinαcosβ
tan(α+β)=tanα+tanβ1tanαtanβ
tan(αβ)=tanαtanβ1+tanαtanβ

Double Angle and Half Angle Formulas

sin(2α)=2sinαcosα
cos(2α)=cos2αsin2α
tan(2α)=2tanα1tan2α
sinα2=±1cosα2−−−−−−−−√
cosα2=±1+cosα2−−−−−−−−√
tanα2=1cosαsinα=sinα1cosα
tanα2=±1+cosα1cosα−−−−−−−−√

Other Useful Trig Formulas

Law of sines

sinαα=sinββ=sinγγ

Law of cosines

a2=b2+c22bccosαb2=a2+c22accosβc2=a2+b22abcosγ

Area of triangle

A=12absinγ
Logarithm Formulas
Hyperbolic Formulas

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Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

Website: http://world4engineers.com