If we construct a triangle in a circle of radius [tex]r[/tex], the radius of the circle will be the hypotenuse of our triangle, and the legs will be [tex]x[/tex] and [tex]y[/tex] as you can see in the picture.
Now we can construct our trigonometric ratios for our triangle as usual:
[tex]sin \alpha = \frac{y}{r} [/tex]
[tex]cos \beta = \frac{x}{r} [/tex]
[tex]tan \beta = \frac{y}{x} [/tex]
[tex]csc \beta = \frac{r}{y} [/tex]
[tex]sec \beta = \frac{r}{x} [/tex]
[tex]cot \beta = \frac{x}{y} [/tex]
As you can see the only two trigonometric functions that don't depend on the value of [tex]r[/tex] are tangent and cotangent.
