Trigonometry Identities

Reciprocal Identity

sin θ=

Reciprocal Identity

Reciprocal Identity

cos θ=

Reciprocal Identity

Reciprocal Identity

tan θ=

Reciprocal Identity

Reciprocal Identity

csc θ=

Reciprocal Identity

Reciprocal Identity

sec θ=

Reciprocal Identity

Reciprocal Identity

cot θ=

Reciprocal Identity

Pythagorean Identity (sin/cos)

1=

Pythagorean Identity

Pythagorean Identity

cos² θ=

Pythagorean Identity

Pythagorean Identity

sin² θ=

Pythagorean Identity

Pythagorean Identity

1 + tan² θ

Pythagorean Identity

Pythagorean Identity

cot² θ + 1=

Pythagorean Identity

Quotient Identity

tan θ=

Quotient Identity

Quotient Identity

cot θ=

Quotient Identity

Pythagorean Identity

tan² θ=

Pythagorean Identity

sec² θ - 1

Pythagorean Identity (sec/tan)

1=

Pythagorean Identity

sec² θ - tan² θ

Pythagorean Identity

cot² θ=

Pythagorean Identity

csc² θ - 1

Pythagorean Identity (csc/cot)

1=

Pythagorean Identity

csc² θ - cot² θ

Even/Odd Identity

sin(-x)=

Even/Odd Identity

-sin x

Even/Odd Identity

cos(-x)=

Even/Odd Identity

cos x

Even/Odd Identity

tan(-x)=

Even/Odd Identity

-tan x

Even/Odd Identity

csc(-x)=

Even/Odd Identity

-csc x

Even/Odd Identity

sec(-x)=

Even/Odd Identity

sec x

Even/Odd Identity

cot(-x)=

Even/Odd Identity

-cot x

Co-Function Identity

cos (π/2-x)=

Co-Function Identity

sin x

Co-Function Identity

sin (π/2-x)=

Co-Function Identity

cos x

Co-Function Identity

tan (π/2-x)=

Co-Function Identity

cot x

Co-Function Identity

cot (π/2-x)=

Co-Function Identity

tan x

Co-Function Identity

csc (π/2-x)=

Co-Function Identity

sec x

Co-Function Identity

sec (π/2-x)=

Co-Function Identity

csc x

Sum/Difference Identity

sin(a+b)=

Sum/Difference Identity

(sin a)(cos b) + (sin b)(cos a)

Sum/Difference Identity

sin(a-b)=

Sum/Difference Identity

(sin a)(cos b) - (sin b)(cos a)

Sum/Difference Identity

cos(a+b)=

Sum/Difference Identity

(cos a)(cos b) - (sin a)(sin b)

Sum/Difference Identity

cos(a-b)=

Sum/Difference Identity

(cos a)(cos b) + (sin a)(sin b)

Sum/Difference Identity

tan(a+b)=

Sum/Difference Identity

Sum/Difference Identity

tan(a-b)=

Sum/Difference Identity

Double Angle Identity

sin(2θ)=

Double Angle Identity

2 sin a cos a

Double Angle Identity

tan(2θ)=

Double Angle Identity

Double Angle Identity

cos(2θ)=

Double Angle Identity

Half Angle Identity

sin(θ/2)=

Half Angle Identity