Trigonometric functions are functions described on an angle. They are used to relate the angles and sides of a triangle. Angles can be defined in degrees or radians. Right triangle is used to understand the trigonometric functions.

In a right triangle, the side opposite to the right angle is called Hypotenuse (H). The side next to or besides the angle (say $\Theta$) and which is common side to both the right angle and defined angle (say $\Theta$) is called the Adjacent angle (A). The side opposite to the angle (say $\Theta$) is called the Opposite angle (O). Hypotenuse is the longest side of the right triangle.

                                         Right Triangle
In Trigonometry, the three main functions are Sine, Cosine and Tangent which are generally written as sin,cos and tan. The formulas for these functions are obtained by dividing the length of one side by another side as follows :

                               $Sine    function: Sin\Theta$ = $\frac{Opposite    Side}{Hypotenuse}$
                               $Cosine    function: cos\Theta$ = $\frac{Adjacent    Side}{Hypotenuse}$
                               $Tangent    function: tan\Theta$ = $\frac{Opposite   Side}{Adjacent Side}$
An easy way to remember these formulas is to remember
            SOHCAHTOA or $S\tfrac{O}{H}C\tfrac{A}{H}T\tfrac{O}{A}$                          
The reciprocals of these functions are not so commonly used. They are :

                    $Cosecant   Function:$ $\frac{1}{sin\Theta }$ = $\frac{Hypotenuse}{Opposite    Side}$
                    $Secant    Function:$ $\frac{1}{cos\Theta }$ = $\frac{Hypotenuse}{Adjacent    Side}$
                    $Cotangent     Function:$ $\frac{1}{tan\Theta }$ = $\frac{Adjacent    Side}{Opposite    Side}$

Generalizing SOHCAHTOA, we have circle definitions for the three trigonometric functions.
              $sin \Theta$ = $\frac{y}{r}$           $cos \Theta$ = $\frac{x}{r}$         $tan \Theta$ = $\frac{y}{x}$