Half Angle Formulas

Proposition (Half-Angle Formulas) The following formulas hold for all angles and where the functions are defined.  

Example (Half-Angle Formulas) Find the exact value of and

    Solution. Since and is in quadrant 1, we have


and





Example (Half-Angle Formulas) Find the exact value of given and is in quadrant 2

    Solution. Since we have Therefore, because is in quadrant 2. Therefore,
    



Example (Half-Angle Formulas) Prove the trigonometric identity:

    Solution. We have,



















Example (Half-Angle Formulas) Solve the equation

    Solution. We have,






    
    
    






    and    

    and  

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Half Angle Formulas
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/half-angle-formulas.html