SOLUTION: How are trigonometric ratios defined?

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Question 951337: How are trigonometric ratios defined?
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
The trigonometric relate the of a right triangle . 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 in a triangle, we name the sides as:
(the side opposite the right angle)
(the side "next to" )
(the side furthest from the angle)
We define the three trigonometrical ratios




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


and the reciprocal ratios:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!












Explanation:


In this right triangle:



Observe the following facts about the right triangle above:

AB is the hypotenuse, which is across
the triangle from the right angle.

BC, the side opposite angle A, is the
side that is across the triangle from angle A.

AC, the side opposite angle B is the
side that is across the triangle from angle B.

BC, the side opposite angle A is 
the same side that is adjacent angle B.

AC, the side adjacent angle A is 
the same side that is opposite angle B.

The definitions of the trigonometric ratios are
as follows:

 


 



---------

 


 



 


Edwin
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