Trigonometric Identities

Flashcards covering trigonometric identities including Pythagorean, even-odd, and quotient identities.

Pythagorean Identity

The equation cos² θ + sin² θ = 1.

First Pythagorean Identity

1 - sin² θ = cos² θ.

Second Pythagorean Identity

1 - cos² θ = sin² θ.

Secant Identity

1 + tan² θ = sec² θ.

Cosecant Identity

cot² θ + 1 = csc² θ.

Cotangent Identity

cot² θ = csc² θ - 1.

Tangent Identity

tan² θ = sec² θ - 1.

Even Function

cos(-x) = cos(x), indicating symmetry about the y-axis.

Odd Function

sin(-x) = -sin(x), indicating symmetry about the origin.

Odd Function for tangent

tan(-x) = -tan(x), indicating symmetry about the origin.

Cosecant Function

csc(-x) = -csc(x), indicating symmetry about the origin.

Secant Function

sec(-x) = sec(x), indicating symmetry about the y-axis.

Cotangent Function

cot(-x) = cot(x), indicating symmetry about the y-axis.

Quotient Identity

tan θ = sin θ / cos θ.

Cotangent Quotient Identity

cot θ = cos θ / sin θ.