Trigonometry XI


   
 
Summary
  •  Trigonometry is that branch of mathematics which deals with the measurements of sides and angles of triangles.
 
          The figure obtained by rotating a given ray about its end point is called an angle.
 
          An angle is called positive if the direction of rotation of ray from initial side to terminal

             side is anti-clockwise.

 
          An angle is called negative if the direction of rotation of ray from initial side to terminal

             side is clockwise.

 
          Sexagesimal system
 
             1 right angle = 90o (degrees)
 
             1 degree = 60' (minutes)
 
             1 minute = 60'' (seconds)
 
          Circular system
 
             The circular measure of an angle is the number of radians it contains where one radian

             is defined as the angle subtended at the centre of a circle by an arc whose length is

             equal to the radius.

 
          180o = p radians .
 
  • The circular measure (q) of the angle subtended at the centre of the circle of radius r by an arc of length l is equal to l/r i.e., q = 1/r.
 
             Each interior angle of a regular polygon of n sides is equal to
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
            
 
            
 
            
 
         
 
         
 
         
 
         
 
         
 
         
 
  • The following rules helps in evaluating t-ratios of the angles:
 
            
 
         
 
         
 
          The positive and negative sign of t-ratios of

             below:

 
 
  • Addition and subtraction formulae
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
  • Transformation of product into sum or difference.
 
         
 
         
 
         
 
         
 
  • Transformation of sum or difference into product
 
         
 
         
 
         
 
         
 
  • T-ratios of multiple and submultiple angles
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
         
 
 
     
   
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