Lesson 9.3: Trigonometric Identities (Adv. Algebra 2/Trigonometry)

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)

Negative Angle Identity

sin(-θ) =

-sin(θ)

Negative Angle Identity

cos(-θ) =

cos(θ)

Negative Angle Identity

tan(-θ) =

-tan(θ)

Negative Angle Identity

csc(-θ) =

-csc(θ)

Negative Angle Identity

sec(-θ) =

sec(θ)

Negative Angle Identity

cot(-θ) =

-cot(θ)

Co-Function Identity

sin(π/2 - θ) =

cos(θ)

Co-Function Identity

cos(π/2 - θ) =

sin(θ)

Co-Function Identity

sec(π/2 - θ) =

csc(θ)

Co-Function Identity

csc(π/2 - θ) =

sec(θ)

Co-Function Identity

tan(π/2 - θ) =

cot(θ)

Co-Function Identity

cot(π/2 - θ) =

tan(θ)

Pythagorean Identity

sin²(θ) + cos²(θ) =

1

Pythagorean Identity

sin²(θ) =

1 - cos²(θ)

Pythagorean Identity

cos²(θ) =

1 - sin²(θ)

Pythagorean Identity

tan²(θ) + 1 =

sec²(θ)

Pythagorean Identity

tan²(θ) =

sec²(θ) - 1

Pythagorean Identity

cot²(θ) + 1 =

csc²(θ)

Pythagorean Identity

cot²(θ) =

csc²(θ) - 1

Pythagorean Identity

1 =

sin²(θ) + cos²(θ)

OR

sec²(θ) - tan²(θ)

OR

csc²(θ) - cot²(θ)