Monday, August 29, 2011

Key Concept of Trigonometric Ratios for cbse class 10

The word trigonometry is a derivation from the Greek language and means measurement of triangles.
Hipparchus, a Greek astronomer and mathematician developed the subject trigonometry.
 The first trigonometric table was compiled by him. He is now known as “the Father of Trigonometry”.
The side that is opposite to the right angle is called the Hypotenuse. This is the longest side in a right triangle.
The side that is opposite to the angle i is called the Opposite side.



The side that runs alongside the angle and which is not the Hypotenuse is called the Adjacent side.


Let 
q   be an acute angle of a right triangle. Then the six trigonometric ratios of q are as follows
sin q  = Hypotenuse/Opposite side
cosec  =Opposite side/Hypotenuse
cos  =Hypotenuse/Adjacent side
sec 
q
 =Adjacent side/Hypotenuse
tan  
 =Adjacent side/Opposite side
cot  
q
 =Opposite side/Adjacent side

Reciprocal Relations

The trigonometric ratios cosec 
q  
 sec 
 and cot 
 are receprocals of sin 
 cos 
 and tan 
respectively.
sin  = 1/cosecq
cos  =1/secq
tan  =1/cot
cosec = 1/sinq
sec =1/cosq
 cot q = 1/ tan q

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