Trigonometry
In a triangle, the ratio of the sides varies with the variation in the angle of the triangle. We can find the relationship between the angles and lengths of sides using trigonometry, a branch of mathematics which deals with the measurement of the angles and the sides of a triangle and of the various relationships existing between them.
Trigonometric Ratios
Let ABC be a rightangled triangle, rightangled at B with âˆ ACB = Î¸. With three sides of the triangle, we can have six different ratios (see Figure). These ratios are given different names. The following table gives the ratios, their names and the relationship between the ratios:
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Figure. A RightAngled Triangle
Figure. A RightAngled Triangle
Ratio Sides 
Name of the Trigonometric Ratio 
Symbol 

sine of Î¸ 
sin Î¸ 

cosine of Î¸ 
cos Î¸ 

tangent of Î¸ 
tan Î¸ 

cotangent of Î¸ 
cot Î¸ 

secant of Î¸ 
sec Î¸ 

cosecant of Î¸ 
cosec Î¸ 
Relationship between trigonometric ratios
 sin Î¸ =
 cos Î¸ =
 tan Î¸ =
Trigonometric Ratios of Standard Angles
The following table gives the trigonometric ratios of standard angles.
Angle Î¸ Ratios 
0Â° 
30Â° 
45Â° 
60Â° 
90Â° 
sin Î¸ 
0 



1 
cos Î¸ 
1 


1/2 
0 
tan Î¸ 
0 

1 

infinity 