Sine function
sin u = y
Cosine function
cos u = x
Tangent function
tan u = y / x
Cotangent function
cot u = x / y
Secant function
sec u = 1 / x
Cosecant function
csc u = 1 / y
Inverse sine function
y = sin^-1 x means x = sin ywhere-1 <= x <= 1and-π / 2 <= y <= π / 2
Inverse cosine function
y = cos^-1 x means x = cos ywhere-1 <= x <= 1and0 <= y <= π
Inverse tangent function
y = tan^-1 x means x = tan ywhere-∞ < x < ∞and-π / 2 < y < π / 2
Inverse cotangent function
y = cot^-1 x means x = cot ywhere-∞ < x < ∞and0 < y < π
Inverse secant function
y = csc^-1 x means x = csc ywhere|x| >= 1and-π / 2 <= y <= π / 2y != 0
Inverse cosecant function
y = sec-1 x means x = sec ywhere|x| >= 1and0 <= y <= πy != π / 2
Pythagorean Identities
sin^2 u + cos^2 u = 1tan^2 u + 1 = sec^2 ucot^2 u + 1 = csc^2 u
Co-Function Identities
sin( π / 2 – u ) = cos ucos( π / 2 – u ) = sin utan( π / 2 – u ) = cot ucsc( π / 2 – u ) = sec usec( π / 2 – u ) = csc ucot( π / 2 – u ) = tan u
Even-Odd Identities
sin(-u) = -sin ucos(-u) = cos utan(-u) = -tan ucsc(-u) = -csc usec(-u) = sec ucot(-u) = -cot u
Reciprocal Identities
csc u = 1 / sin usec u = 1 / cos ucot u = 1 / tan u
Quotient Identities
tan u = sin u / cos ucot u = cos u / sin u