Chapter 7: Small Angles & Approximation

7.1  Derivation of formulae

In the diagram, OA and OB are radii and the tangent at A meets OB produced at D.

If OA = 1 = OB & q is measured in radians, then

OC = cos q
AC = sin q
AD = tan q
arc AB = q
When q is small, OC » OB & AC » arc AB »AD.

Hence, cos q » 1 & sin q » q » tan q.
 
 
 
 
      
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