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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