Question 951337
The {{{six}}} trigonometric {{{ratios}}} relate the {{{sides}}} of a right triangle {{{to}}} {{{its}}} {{{angles}}}. Specifically, they are ratios of two sides of a right triangle and a related angle. 

Trigonometric functions are typically used to calculate unknown lengths or angles in a right triangle. 
The six functions are all related and can be defined in terms of one another.


For the angle {{{theta}}} in a {{{right-angled}}} triangle, we name the sides as:

    {{{hypotenuse}}} (the side opposite the right angle)
    {{{adjacent}}} (the side "next to" {{{theta}}})
    {{{opposite}}} (the side furthest from the angle)

We define the three trigonometrical ratios 
{{{sin (theta)=hypotenuse/opposite}}}
{{{cos(theta)=adjacent/hypotenuse}}}		
{{{tan (theta)=opposite/adjacent}}}


To remember these, many people use {{{SOH}}}(S stands for sin, O for opposite, and H for hypotenuse) {{{CAH}}} {{{TOA}}}, that is:

    {{{sin(theta) = O[pposite]/H[ypotenuse]}}},

   {{{cos (theta) = A[djacent]/H[ypotenuse]}}}, and

   {{{tan (theta)  = O[pposite]/A[djacent]}}}


and  the reciprocal ratios:
	

{{{csc(theta) =hypotenuse/opposite=1/sin(theta)}}}	
{{{sec(theta)=hypotenuse/adjacent=1/cos(theta)}}}		
{{{cot(theta) =adjacent/opposite=1/tan(theta)}}}