Trigonomietric Identities

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Trigonometry

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Trigonometry

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Trigonomic Functions & Identities

Trigonometric Identities

Quotient Identities

tan u = sin u / cos u

cot u = cos u / sin u

Reciprocal Identities

csc u = 1 / sin u

sec u = 1 / cos u

cot u = 1 / tan u

Even-Odd Identities

sin(-u) = -sin u

cos(-u) = cos u

tan(-u) = -tan u

csc(-u) = -csc u

sec(-u) = sec u

cot(-u) = -cot u

Co-Function Identities

sin( π / 2 – u ) = cos u

cos( π / 2 – u ) = sin u

tan( π / 2 – u ) = cot u

csc( π / 2 – u ) = sec u

sec( π / 2 – u ) = csc u

cot( π / 2 – u ) = tan u

Pythagorean Identities

sin^2 u + cos^2 u = 1

tan^2 u + 1 = sec^2 u

cot^2 u + 1 = csc^2 u

Inverse Trigonometric Functions

Inverse cosecant function

y = sec-1 x means x = sec y

where

|x| >= 1

and

0 <= y <= π

y != π / 2

Inverse secant function

y = csc^-1 x means x = csc y

where

|x| >= 1

and

-π / 2 <= y <= π / 2

y != 0

Inverse cotangent function

y = cot^-1 x means x = cot y

where

-∞ < x < ∞

and

0 < y < π

Inverse tangent function

y = tan^-1 x means x = tan y

where

-∞ < x < ∞

and

-π / 2 < y < π / 2

Inverse cosine function

y = cos^-1 x means x = cos y

where

-1 <= x <= 1

and

0 <= y <= π

Inverse sine function

y = sin^-1 x means x = sin y

where

-1 <= x <= 1

and

-π / 2 <= y <= π / 2

Trigonometric Functions

Cosecant function

csc u = 1 / y

Secant function

sec u = 1 / x

Cotangent function

cot u = x / y

Tangent function

tan u = y / x

Cosine function

cos u = x

Sine function

sin u = y