Trigonometric Identities: Negative Angles, Complementary Angles, and Reciprocals (Vocabulary Cards)

Vocabulary-style flashcards covering negative-angle identities, co-function relationships, fundamental identities, and reciprocal definitions.

cos(-θ)

Cosine is even; cos(-θ) = cos θ.

sec(-θ)

Secant is even; sec(-θ) = sec θ.

sin(-θ)

Sine is odd; sin(-θ) = -sin θ.

csc(-θ)

Cosecant is odd; csc(-θ) = -csc θ.

tan(-θ)

Tangent is odd; tan(-θ) = -tan θ.

cot(-θ)

Cotangent is odd; cot(-θ) = -cot θ.

cos(90° − θ)

Cosine of a complementary angle equals sine: cos(90°−θ) = sin θ.

sec(90° − θ)

Secant of a complementary angle equals cosecant: sec(90°−θ) = csc θ.

sin(90° − θ)

Sine of a complementary angle equals cosine: sin(90°−θ) = cos θ.

csc(90° − θ)

Cosecant of a complementary angle equals secant: csc(90°−θ) = sec θ.

tan(90° − θ)

Tangent of a complementary angle equals cotangent: tan(90°−θ) = cot θ.

cot(90° − θ)

Cotangent of a complementary angle equals tangent: cot(90°−θ) = tan θ.

cos(π/2 − θ)

Cosine of a complementary angle (radians) equals sine: cos(π/2−θ) = sin θ.

sec(π/2 − θ)

Secant of a complementary angle equals cosecant: sec(π/2−θ) = csc θ.

sin(π/2 − θ)

Sine of a complementary angle equals cosine: sin(π/2−θ) = cos θ.

csc(π/2 − θ)

Cosecant of a complementary angle equals secant: csc(π/2−θ) = sec θ.

tan(π/2 − θ)

Tangent of a complementary angle equals cotangent: tan(π/2−θ) = cot θ.

cot(π/2 − θ)

Cotangent of a complementary angle equals tangent: cot(π/2−θ) = tan θ.

tan θ = sin θ / cos θ

Tangent equals sine divided by cosine.

cot θ = cos θ / sin θ

Cotangent equals cosine divided by sine.

sin^2 θ + cos^2 θ = 1

Pythagorean identity: sine squared plus cosine squared equals 1.

1 + tan^2 θ = sec^2 θ

Pythagorean identity relating tan and sec.

1 + cot^2 θ = csc^2 θ

Pythagorean identity relating cot and csc.

csc θ = 1 / sin θ

Cosecant equals reciprocal of sine.

sec θ = 1 / cos θ

Secant equals reciprocal of cosine.

cot θ = 1 / tan θ

Cotangent equals reciprocal of tangent.

sin θ = 1 / csc θ

Sine equals reciprocal of cosecant.

cos θ = 1 / sec θ

Cosine equals reciprocal of secant.

tan θ = 1 / cot θ

Tangent equals reciprocal of cotangent.