Fundamental Identities

Even/Odd Identity for Cosine

cos(-θ)=cosθ

Double-Angle Formula for Cosine

cos(2u)=cos²(u)-sin²(u)=2cos²(u)-1=1-2sin²(u)

Sum Formula for Cosine

cos(u+v)=cos(u) cos(v)-sin(u) sin(v)

Difference Formula for Cosine

cos(u-v)=cos(u) cos(v)+sin(u) sin(v)

Reciprocal Identity for Cosine

cosθ=1/secθ

Cofunction Identity for Cosine

cosθ=sin(90-θ)

Even/Odd Identity for Cotangent

cot(-θ)=-cotθ

Pythagorean Identity for Cotangent and Cosecant

cot²θ+1=csc²θ

Reciprocal Identity for Cotangent

cotθ=1/tanθ

Quotient Identity for Sine, Cosine, and Cotangent

cotθ=cosθ/sinθ

Cofunction Identity for Cotangent

cotθ=tan(90-θ)

Even/Odd Identity for Cosecant

csc(-θ)=-cscθ

Reciprocal Identity for Cosecant

cscθ=1/sinθ

Cofunction Identity for Cosecant

cscθ=sec(90-θ)

Even/Odd Identity for Secant

sec(-θ)=secθ

Reciprocal Identity for Secant

secθ=1/cosθ

Cofunction Identity for Secant

secθ=csc(90-θ)

Even/Odd Identity for Sine

sin(-θ)=-sinθ

Double-Angle Formula for Sine

sin(2u)=2sin(u) cos(u)

Sum Formula for Sine

sin(u+v)=sin(u) cos(v)+cos(u) sin(v)

Difference Formual for Sine

sin(u-v)= sin(u) cos (v)-cos(u) sin(v)

Pythagorean Identity for Sine and Cosine

sin²θ+cos²θ=1

Reciprocal Identity for Sine

sinθ=1/cscθ

Cofunction Identity for Sine

sinθ=cos(90-θ)

Even/Odd Identity for Tangent

tan(-θ)=-tanθ

Sum Formula for Tangent

tan(u+v)=tan(u)+tan(v)/1-tan(u) tan(v)

Difference Formula for Tangent

tan(u-v)=tan(u)-tan(v)/1+tan(u) tan(v)

Double-Angle Formula for Tangent

tan2u=2tan(u)/1-tan²(u)

Pythagorean Identity for Tangent and Secant

tan²θ+1=sec²θ

Reciprocal Identity for Tangent

tanθ=1/cotθ

Cofunction Identity for Tangent

tanθ=cot(90-θ)

Quotient Identity for Sine, Cosine, and Tangent

tanθ=sinθ/cosθ