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trig identities

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 xcot (90° – x) = tan x
 sec (90° – x) = csc xcsc (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

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