Fundamental Trigonometric Identities

Reciprocal Identity; sin θ

1/csc θ

Reciprocal Identity; cos θ

1/sec θ

Reciprocal Identity; tan θ

1/cot θ

Reciprocal Identity; csc θ

1/sin θ

Reciprocal Identity; sec θ

1/cos θ

Reciprocal Identity; cot θ

1/tan θ

Quotient Identity; tan θ

sin θ/cos θ

Quotient Identity; cot θ

 cos θ/ sin θ

Pythagorean Identity; 1

sin^2 θ + cos^2 θ

Pythagorean Identity; sec^2 θ

1 + tan^2 θ

Pythagorean Identity; csc^2 θ

1 + cot^2 θ

Cofunction Identity; cos θ

sin (π/2 - θ)

Cofunction Identity; sin θ

cos (π/2 - θ)

Cofunction Identity; cot θ

tan (π/2 - θ)

Cofunction Identity; csc θ

sec (π/2 - θ)

Cofunction Identity; sec θ

csc (π/2 - θ)

Cofunction Identity; tan θ

cot (π/2 - θ)

Even/Odd Identity; -sin θ

sin (-θ)

Even/Odd Identity; cos θ

cos (-θ)

Even/Odd Identity; -tan θ

tan (-θ)

Even/Odd Identity; -csc θ

csc (-θ)

Even/Odd Identity; sec θ

sec (-θ)

Even/Odd Identity; -cot θ

cot (-θ)

Law of Sines

Sin(A)/a=Sin(B)/b=Sin(C)/c

Law of Cosines(C)

c²=a²+b²-2ab(Cos(C))

Law of Cosines(B)

b²=a²+c²-2ab(Cos(B))

Law of Cosines(A)

a²=b²+c²-2ab(Cos(A))

Law of Sines(height)

bSin(A)

Double-angle identities, Sin(2U)

2Sin(u)Cos(u)

Double-angle identities, Cos(2U)1

Cos²(u)-Sin²(u)

Double-angle identities, Cos(2U)

1-2Sin²(u)

Double-angle identities, Tan(2U)

2Tan(u)/1-Tan²(u)

Sum/Difference identities, Sin(u+v)

(Sin(u)*Cos(v))+(Sin(v)*Cos(u))

Sum/Difference identities, Sin(u-v)

(Sin(u)*Cos(v))-(Sin(v)*Cos(u))

Sum/Difference identities, Cos(u-v)

(Cos(u)*Cos(v))+(Sin(u)*Sin(v))

Sum/Difference identities, Cos(u+v)

(Cos(u)*Cos(v))-(Sin(u)*Sin(v))

Sum/Difference identities, Tan(u+v)

(Tan(u)-Tan(v))/(1+Tan(u)*Tan(v))

Sum/Difference identities, Tan(u-v)

(Tan(u)+Tan(v))/(1-Tan(u)*Tan(v))