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Trig Cheat Sheet by

math

Reciprocal Identities

csc θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ

Pythag­orean Identities

sin²θ + cos²θ = 1
sec²θ = 1 + tan²θ
csc²θ = 1 + cot²θ

Addition & Subtra­ction Formulas

sin(α±β) = sin(α) cos(β) ± sin(β) cos(α)
cos(α±β) = cos(α) cos(β) ∓ sin(β) sin(α)
tan(α±β) = tan(α) ± tan(β)
      ­     1 ∓ tan(α) tan(β)
 

Corelated Angle Identities

sin(π/2 ± θ) = cos (θ)
cos(π/2 ± θ) = ∓sin (θ)
tan(π/2 ± θ) = ∓cot (θ)

sin(3π/2 ± θ) = -cos (θ)
cos(3π/2 ± θ) = ±sin (θ)
tan(3π/2 ± θ) = ∓cot (θ)

Double Angle Formulas

sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
      ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­    = 2 cos²(θ) - 1
      ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­    = 1 - 2 sin²(θ)
tan(2θ) = 2 tan(θ)
      ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­   ­    1 - tan²(θ)
 

Quotient Identities

tan θ = sin θ/cos θ
cot θ = cos θ/sin θ

Related Angle Identities

sin(π ∓ θ) = ±sin(θ)
cos(π ∓ θ) = -cos(θ)
tan(π ∓ θ) = ∓tan(θ)

sin(2π - θ) = -sin(θ)
cos(2π - θ) = cos(θ)
tan(2π - θ) = -tan(θ)

sin(-θ) = -sin(θ)
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)

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