Trigonometric Relationships and Identities



Trigonometric Functions and Identities

Reciprocal Identities

csc t = 1

sin t

sec t = 1

cos t

cot t = 1

tan t

Even Trigonometric Functions

cos (– t) = cos t

sec (– t) = sec t

Odd Trigonometric Functions

sin (– t) = – sin t

csc (– t) = – csc t

tan (– t) = – tan t

cot (– t) = – cot t

Pythagorean Identities

sin2 t + cos2 t = 1 1 + tan2 t = sec2 t 1 + cot2 t = csc2 t

Quotient Identities

tan t = sin t cot t = cos t

cos t sin t

Cofunction Identities

sin t = cos (90o – t) and cos t = sin (90o – t)

tan t = cot (90o – t) and cot t = tan (90o – t)

sec t = csc (90o – t) and csc t = sec (90o – t)

Periodic Properties of the Sine, Cosine, Tangent, and Cotangent Functions

sin (t + 2π) = sin t

cos (t + 2π) = cos t

tan (t + π) = tan t

cot (t + π) = cot t

Repetitive Behavior of the Sine, Cosine, and Tangent Functions

sin (t + 2πn) = sin t

cos (t + 2πn) = cos t

tan (t + πn) = tan t

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