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