Multiple Angle Formulas

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

Example (Multiple Angle Formulas) Find the exact value of given and is in quadrant 3.

    Solution. We have,




Example (Multiple Angle Formulas) Find the exact value of given and is in quadrant 3.

    Solution. Since and is in quadrant 3, we have and thus so Therefore,




Example (Multiple Angle Formulas) Prove the trigonometric identity:

    Solution. We have,















Example (Multiple Angle Formulas) Solve the equation

    Solution. Let be any integer. We have,













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