Trig Identities To Know

Reciprocal Identities

sin u = 1/csc u; csc u = 1/sin u

cos u = 1/sec u; sec u = 1/cos u

tan u = 1/cot u ; cot u = 1/tan u

Quotient Identities

tan u = sin u/cos u

cot u = cos u/ sin u

Pythagorean Identities

sin²u + cos²u = 1

1 + tan²u = sec²u   (The last two can be derived from the first)

1 + cot²u = csc²u

Co-Function Identities

sin(p/2 - u) = cos u

cos (p/2 - u) = sin u

tan (p/2 - u) = cotu

cot (p/2 - u) = tan u

sec (p/2 - u) = csc u

csc (p/2 - u) = sec u

Odd/Even Identities

sin(- u) = -sin u

csc (- u) = -csc u

cos (- u) = cos u

sec (- u) = sec u

tan (- u) = -tan u

cot (- u) = -cot u