[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse}
=\cfrac{y}{r}
=\cfrac{1}{csc(\theta)}
\\ \quad \\\\
% cosine
cos(\theta)=\cfrac{adjacent}{hypotenuse}
=\cfrac{x}{r}
=\cfrac{1}{sec(\theta)}
\\ \quad \\\\
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
=\cfrac{y}{x}
=\cfrac{sin(\theta)}{cos(\theta)}[/tex]
[tex]\bf cot(\theta)=\cfrac{adjacent}{opposite}
=\cfrac{x}{y}
=\cfrac{cos(\theta)}{sin(\theta)}
\\ \quad \\\\
% cosecant
csc(\theta)=\cfrac{hypotenuse}{opposite}
=\cfrac{r}{y}
=\cfrac{1}{sin(\theta)}
\\ \quad \\\\
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}
=\cfrac{r}{x}
=\cfrac{1}{cos(\theta)}\\\\
-------------------------------\\\\
P(x,y)\implies \delta\qquad tan(\delta)=\cfrac{y}{x}[/tex]
