Six Trig Finctions

r/Y

Pythagorean: csc^2 u = 1 + cot^2 u

Reciprocal: csc u = 1/sin u

r/X

Pythagorean: sec^2 u = 1 + tan^2 u

Reciprocal: sec u = 1/ cos u

X/Y

Pythagorean: 1 + cot^2 u = csc^2 u

Reciprocal: cot u = 1/tan u

Y/r

Pythagorean: sine^2 u + cosine^2u=1

Reciprocal: sine u=1/cosine u

Half Angle: sine^2 u=1-cosine(2u)/2

X/r

Pythagorean: sine^2 u + cosine^2u=1

Reciprocal: cos u=1/sec u

Half Angle: cosine^2 u=1+cosine(2u)/2

Y/X

Pythagorean: 1+tan^2u=sec^2u

Reciprocal: tan u=1/cot u

Half Angle: tan^2 u=1-cos(2u)/1+cosine(2u)