We say that sine, cossine and tangent are angle's properties. All of these identitites are born from similar triangles (right-angled triangles). Initially we use it to calculate sides of triangles without needing another, like in the cases where we have at least two triangles to calculate it by proportionality. You want to see how it works, draw two similar right triangles or more if you want to, do the similarity of triangles with two of them, after that, isolate in the left hand side of the equation informations about the first triangle, and in the right hand side informations about the second one . You'll see that both of them share a property in common: the ratio of two sides of a triangle equals the ratio of the respective both sides in the other one. And we give that property to the angle that they share, because if it changes, they won't be similar, and if they're not similar, we can't do proportionality.