Identities

sin(pi/2 - x)

cos(x) =

cofunction

tan(pi/2 - x)

cot(x) =

cofunction

sec(pi/2 - x)

csc(x) =

cofunction

cos(pi/2 - x)

sin(x) =

cofunction

cot(pi/2 - x)

tan(x) =

cofunction

csc(pi/2 - x)

sec(x) =

cofunction

-sin(x)

sin(-x) =

even odd

cos(x)

cos(-x) =

even odd

-tan(x)

tan(-x) =

even odd

-csc(x

csc(-x) =

even odd

-cot(x)

cot(-x) =

even odd

sec(x)

sec(-x) =

even odd

1 / csc(x)

sin(x) =

reciprocal

1 / sec(x)

cos(x) =

reciprocal

1 / cot(x)

tan(x) =

reciprocal

1 / sin(x)

csc(x) =

reciprocal

1 / cos(x)

sec(x) =

reciprocal

1 / tan(x)

cot(x) =

reciprocal

sin(x) / cos(x)

tan(x) =

quotient

cos(x) / sin(x)

cot(x) =

quotient

cos²x + sin²x

1 =

pythagorean

tan²x + 1

sec²x =

pythagorean

cot²x + 1

csc²x =

pythagorean

sin(x)cos(y) + cos(x)sin(y)

sin(x+y) =

sum difference

sin(x)cos(y) - cos(x)sin(y)

sin(x-y) =

sum difference

[tan(x) + tan(y)] / [1 + tan(x)tan(y)]

tan(x+y) =

sum difference

cos(x)cos(y) - sin(x)sin(y)

cos(x+y) =

sum difference

cos(x)cos(y) + sin(x)sin(y)

cos(x-y) =

sum difference

[tan(x) - tan(y)] / [1 + tan(x)tan(y)]

tan(x-y) =

sum difference

2sin(x)cos(x)

sin(2x) =

double angle

cos²x - sin²x

cos(2x) =

double angle

[2tan(x)] / [1 - tan²x]

tan(2x) =

double angle

± sqrt{ [1 - cos(x)] / 2 }

sin(x/2) =

half angle

± sqrt{ [1 + cos(x)] / 2 }

cos(x/2) =

half angle

[1 - cos(x)] / sin(x)

tan(x/2) =

half angle 1

sin(x) / [1 + cos(x)]

tan(x/2) =

half angle 2