# Trigonometric Formulas

Posted By on December 21, 2014

### Right-Triangle Definitions

 sinα=OppositeHypotenuse
 cscα=1sinα=HypotenuseOpposite

### Reduction Formulas

 sin(−x)=−sin(x)
 cos(−x)=cos(x)
 sin(π2−x)=cos(x)
 cos(π2−x)=sin(x)
 sin(π2+x)=cos(x)
 cos(π2+x)=−sin(x)
 sin(π−x)=sin(x)
 cos(π−x)=−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)=sinα⋅cosβ+sinβ⋅cosα
 sin(α−β)=sinα⋅cosβ−sinβ⋅cosα
 cos(α+β)=cosα⋅cosβ−sinα⋅cosβ
 cos(α−β)=cosα⋅cosβ+sinα⋅cosβ
 tan(α+β)=tanα+tanβ1−tanα⋅tanβ
 tan(α−β)=tanα−tanβ1+tanα⋅tanβ

### Double Angle and Half Angle Formulas

 sin(2α)=2⋅sinα⋅cosα
 cos(2α)=cos2α−sin2α
 tan(2α)=2tanα1−tan2α
 sinα2=±1−cosα2−−−−−−−−√
 cosα2=±1+cosα2−−−−−−−−√
 tanα2=1−cosαsinα=sinα1−cosα
 tanα2=±1+cosα1−cosα−−−−−−−−√

### Other Useful Trig Formulas

Law of sines

 sinαα=sinββ=sinγγ

Law of cosines

 a2=b2+c2−2⋅b⋅c⋅cosαb2=a2+c2−2⋅a⋅c⋅cosβc2=a2+b2−2⋅a⋅b⋅cosγ

Area of triangle

 A=12absinγ

#### Posted by Akash Kurup

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

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