Trigonometric Identities and Formulas: Sine, Cosine, Tangent, and Half-Angles

sin θ

1 / csc θ

csc θ

1 / sin θ

cos θ

1 / sec θ

sec θ

1 / cos θ

tan θ

1 / cot θ

cot θ

1 / tan θ

sin²θ + cos²θ

1

1 + tan²θ

sec²θ

1 + cot²θ

csc²θ

sin(-θ)

-sin θ

cos(-θ)

cos θ

tan(-θ)

-tan θ

csc(-θ)

-csc θ

sec(-θ)

sec θ

cot(-θ)

-cot θ

sin(α + β)

sin α cos β + cos α sin β

cos(α + β)

cos α cos β - sin α sin β

tan(α + β)

(tan α + tan β) / (1 - tan α tan β)

sin(α - β)

sin α cos β - cos α sin β

cos(α - β)

cos α cos β + sin α sin β

tan(α - β)

(tan α - tan β) / (1 + tan α tan β)

sin 2θ

2 sin θ cos θ

cos 2θ (version 1)

cos²θ - sin²θ

cos 2θ (version 2)

2 cos²θ - 1

cos 2θ (version 3)

1 - 2 sin²θ

tan 2θ

(2 tan θ) / (1 - tan²θ)

sin(θ/2)

±√[(1 - cos θ)/2]

cos(θ/2)

±√[(1 + cos θ)/2]

tan(θ/2) version 1

±√[(1 - cos θ)/(1 + cos θ)]

tan(θ/2) version 2

(1 - cos θ) / sin θ

tan(θ/2) version 3

sin θ / (1 + cos θ)

sin(π/2 - x)

cos x

cos(π/2 - x)

sin x

sin(π - x)

sin x

sin(3π/2 + x)

-cos x