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Trigonometric Function Identities, Cheat Sheet of Trigonometry

Greenville Technical CollegeTrigonometry

A list of trigonometric function identities, including identities for sin, cos, tan, csc, sec, and cot. Each identity is presented as a function of an angle θ, along with its reciprocal and inverse. These identities are essential in advanced mathematics and physics, particularly in solving equations and calculating values of trigonometric functions.

Typology: Cheat Sheet

2020/2021

Uploaded on 07/22/2021

Jkreid50
Jkreid50 🇺🇸

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Function sin cos tan
sinθsinθ√(1-cos2θ) tanθ/ √(1+tan2θ)
cosθ√(1-sin2θ) cosθ1/ √(1+tan2θ)
tanθsinθ/ √(1-sin2θ) √(1-cos2θ) / cosθtanθ
cscθ1 / sinθ1/√(1-cos2θ) √(1+tan2θ) / tanθ
secθ1 / √(1-sin2θ) 1 / cosθ√(1+tan2θ)
cotθ√(1-sin2θ) / sinθcosθ/ √(1-cos2θ) 1 / tanθ
Function csc sec cot
sinθ1 / cscθ√(sec2θ- 1) / secθ1 / √(1 + cot2θ)
cosθ√(csc2θ- 1) / csc2θ1 / secθcotθ/ √(1 + cot2θ)
tanθ1 / √(csc2θ- 1) √(sec2θ- 1) 1 / cotθ
cscθcscθsecθ /√(sec2θ- 1) √(1 + cot2θ)
secθcscθ/ √(csc2θ- 1) secθ√(1 + cot2θ) / cotθ
cotθ√(csc2θ- 1) 1 / √(sec2θ- 1) cotθ

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Function sin cos tan sin θ sin θ √(1-cos^2 θ ) tan θ / √(1+tan^2 θ ) cos θ √(1-sin^2 θ ) cos θ 1 / √(1+tan^2 θ ) tan θ sin θ / √(1-sin^2 θ ) √(1-cos^2 θ ) / cos θ tan θ csc θ 1 / sin θ 1/√(1-cos^2 θ ) √(1+tan^2 θ ) / tan θ sec θ 1 / √(1-sin^2 θ ) 1 / cos θ √(1+tan^2 θ ) cot θ √(1-sin^2 θ ) / sin θ cos θ / √(1-cos^2 θ ) 1 / tan θ Function csc sec cot sin θ 1 / csc θ √(sec^2 θ - 1) / sec θ 1 / √(1 + cot^2 θ ) cos θ √(csc^2 θ - 1) / csc^2 θ 1 / sec θ cot θ / √(1 + cot^2 θ ) tan θ 1 / √(csc^2 θ - 1) √(sec^2 θ - 1) 1 / cot θ csc θ csc θ sec θ / √(sec^2 θ - 1) √(1 + cot^2 θ ) sec θ csc θ / √(csc^2 θ - 1) sec θ √(1 + cot^2 θ ) / cot θ cot θ √(csc^2 θ - 1) 1 / √(sec^2 θ - 1) cot θ