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Trig Identities

Identities involving trig functions are listed below.

 

Pythagorean Identities

sin2 θ + cos2 θ = 1

tan2 θ + 1 = sec2 θ

cot2 θ + 1 = csc2 θ

Reciprocal Identities

Ratio Identities

 

Odd/Even Identities

sin (–x) = –sin x

cos (–x) = cos x

tan (–x) = –tan x

csc (–x) = –csc x

sec (–x) = sec x

cot (–x) = –cot x

 

Cofunction Identities, radians

  Cofunction Identities, degrees
 

sin (90° – x) = cos x

cos (90° – x) = sin x

  tan (90° – x) = cot x cot (90° – x) = tan x
  sec (90° – x) = csc x csc (90° – x) = sec x

 

Periodicity Identities, radians

  Periodicity Identities, degrees

sin (x + 2π) = sin x

csc (x + 2π) = csc x

 

sin (x + 360°) = sin x

csc (x + 360°) = csc x

cos (x + 2π) = cos x

sec (x + 2π) = sec x

 

cos (x + 360°) = cos x

sec (x + 360°) = sec x

tan (x + π) = tan x

cot (x + π) = cot x

 

tan (x + 180°) = tan x

cot (x + 180°) = cot x

 

Sum/Difference Identities

 

Double Angle Identities

 

Half Angle Identities

  or  

  or  

  or    or  

 

Product to Sum Identities

 

Sum to Product Identities

 

See also

Sine, cosine, tangent, cosecant, secant, cotangent

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes