Calculus 3 Trigonometric Identities Review

csc u =

1 / sin u

cot u =

1 / tan u

sec u =

1 / cos u

first pythagorean identity

sin²u + cos²u = 1

second pythagorean identity

1 + tan²u = sec²u

third pythagorean identity

1 + cot²u = csc²u

sin u / cos u =

tan u

cos u / sin u =

cot u

sin(pi/2 - u) =

cos u

tan(pi/2 - u) =

cot u

csc(pi/2 - u) =

sec u

cos(pi/2 - u) =

sin u

cot(pi/2 - u) =

tan u

sec(pi/2 - u) =

csc u

sin(-u) =

-sin u

tan(-u) =

-tan u

csc(-u) =

-csc u

cos(-u) =

cos u

cot(-u) =

-cot u

sec(-u) =

sec u

sin(u +- v) =

sin u cos v +- cos u sin v

cos(u +- v) =

cos u cos v -+ sin u sin v

tan(u +- v) =

(tan u +- tan v) / (1 -+ tan u tan v)

sin(2u) =

2 sin u cos u

cos(2u) =

cos²u - sin²u OR 2 cos²u - 1 OR 1 - 2sin²u

tan(2u) =

(2 tan u) / (1 - tan²u)

sin²u =

[1 - cos(2u)] / 2

cos²u =

[1 + cos (2u)] / 2

tan²u =

[1 - cos(2u)] / [1 + cos(2u)]