Trigonometry Function Identities
Quotient Identities
tanθ =
cotθ =
Reciprocal Indentities
sinθ =
sinθ
cosθ
1
cscθ
1
secθ
1
tanθ =
cotθ
cosθ =
cosθ
sinθ
Pythagorean Identities
cscθ =
1
sinθ
1
cosθ
1
cotθ =
tanθ
secθ =
Even/Odd Indentities
sin2θ + cos2θ = 1
sin(-θ) = -sinθ
cos(-θ) = cosθ
2
2
sec θ - tan θ = 1
tan(-θ) = -tanθ
cot(-θ) = -cotθ
2
2
csc θ - cot θ = 1
csc(-θ) = -cscθ
sec(-θ) = secθ
Cofunction Identities
Sum/Difference Indentities
sin � - θ = cosθ
2
cos � - θ = sinθ
2
tan � - θ = cotθ
2
cot
� - θ = tanθ
2
csc � - θ = secθ
sec � - θ = cscθ
2
2
� radians = 90°
2
Double Angle Identities
sin(θ ± ɸ) = sinθ cosɸ ± cosθ sinɸ
cos(θ ± ɸ) = cosθ cosɸ
tan(θ ± ɸ) =
±
sinθ sinɸ
tanθ ± tan ɸ
±
1 tanθ tan ɸ
Half Angle Indentities
sin(2θ) = 2 sinθ cosθ
2
sin θ =
2
2
cos(2θ) = cos θ - sin θ
1 - cos(2θ)
2
1 + cos(2θ)
2
1 - cos(2θ)
tan2θ =
1 + cos(2θ)
2
cos(2θ) = 2 cos θ - 1
cos2θ =
2
cos(2θ) = 1 - 2 sin θ
2 tanθ
tan(2θ) =
2
1 - tan θ
Sum to Product of Two Angles
Product to Sum of Two Angles
sinθ + sinɸ = 2sin
θ+ɸ
θ-ɸ
cos
2
2
sinθ sinɸ =
[cos(θ - ɸ) - cos(θ + ɸ)]
2
sinθ - sinɸ = 2cos
θ+ɸ
θ-ɸ
sin
2
2
cosθ cosɸ =
[cos(θ - ɸ) + cos(θ + ɸ)]
2
cosθ + cosɸ = 2cos
θ+ɸ
θ-ɸ
cos
2
2
sinθ cosɸ =
[sin(θ + ɸ) + sin(θ - ɸ)]
2
cosθ - cosɸ = -2sin
θ+ɸ
sin
2
cosθ sinɸ =
[sin(θ + ɸ) + sin(θ - ɸ)]
2
θ-ɸ
2