The square on the hypotenuse is equal to the sum of the squares on the other two sides.

which gives:

a^{2} = b^{2} + c^{2}

from which we can derive the following relationships between the trig functions:

sin^{2}(θ)
+ cos^{2}(θ)
= 1

sin^{2}(θ)
= 1 + tan^{2}(θ)

cosec^{2}(θ)
= 1 + cot^{2}(θ)