Trigonometric formulas

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  • 7. Angle sum and difference identities
    These are also known as the  addition and subtraction theorems  or  formulae . The identities can be derived by combining right triangles ...
  • 6. Symmetry, shifts, and periodicity
    By examining the unit circle, the following properties of the trigonometric functions can be established. Symmetry When the trigon...
  • 18. Identities without variables
    The curious identity known as Morrie's law {\displaystyle \cos 20^{\circ }\cdot \cos 40^{\circ }\cdot \cos 80^{\circ }={\frac {1}{8}}}...

Tuesday, November 29, 2016

3. Inverse functions

Main article: Inverse trigonometric functions

The inverse trigonometric functions are partial inverse functions for the trigonometric functions. For example, the inverse function for the sine, known as the inverse sine (sin^−1) or arcsine (arcsin or asin), satisfies


at November 29, 2016
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  • and periodicity
  • Angle sum and difference identities
  • Angles
  • Calculus
  • Certain linear fractional transformations
  • Composition of trigonometric functions
  • Exponential definitions
  • Historical shorthands
  • Identities without variables
  • Infinite product formulae
  • Inverse functions
  • Inverse trigonometric functions
  • Lagrange's trigonometric identities
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  • Multiple-angle formulae
  • Other sums of trigonometric functions
  • Power-reduction formula
  • Product-to-sum and sum-to-product identities
  • Pythagorean identity
  • Relation to the complex exponential function
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  • Symmetry
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Trigonometric formulas

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      • 2. Trigonometric functions
      • 3. Inverse functions
      • 4. Pythagorean identity
      • 5. Historical shorthands
      • 6. Symmetry, shifts, and periodicity
      • 7. Angle sum and difference identities
      • 8. Multiple-angle formulae
      • 9. Power-reduction formula
      • 10. Product-to-sum and sum-to-product identities
      • 11. Linear combinations
      • 12. Lagrange's trigonometric identities
      • 13. Other sums of trigonometric functions
      • 14. Certain linear fractional transformations
      • 15. Inverse trigonometric functions
      • 16. Relation to the complex exponential function
      • 17. Infinite product formulae
      • 18. Identities without variables
      • 19. Composition of trigonometric functions
      • 20. Calculus
      • 21. Exponential definitions
      • 22. Miscellaneous

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