Trigonometric Identities

Front

What is the definition of secant (sec) in trigonometry?

Back

Secant is the reciprocal of cosine: sec(θ) = 1/cos(θ).

Front

What is the definition of tangent (tan) in trigonometry?

Back

Tangent is the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ).

Front

What is the Pythagorean identity involving sine and cosine?

Back

sin²(θ) + cos²(θ) = 1.

Front

What is the relationship between secant and tangent?

Back

sec²(θ) = 1 + tan²(θ).

Front

What is the definition of cotangent (cot) in trigonometry?

Back

Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ) = cos(θ)/sin(θ).

Front

What is the definition of cosecant (csc) in trigonometry?

Back

Cosecant is the reciprocal of sine: csc(θ) = 1/sin(θ).

Front

What is the identity for secant squared minus tangent squared?

Back

sec²(θ) - tan²(θ) = 1.

Front

What is the product of (secθ - 1)(secθ + 1)?

Back

(secθ - 1)(secθ + 1) = tan²(θ).

Front

How do you simplify tan(x)/sin(x) + sec(x)?

Back

tan(x)/sin(x) + sec(x) = 2sec(x).

Front

What is the definition of cotangent squared (cot²)?

Back

cot²(θ) = cos²(θ)/sin²(θ).