Inverse Trigonometry

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Important Formulas:


1.  As   is a objective function, its inverse is given by   where and This function is called the arc sine function and is denoted by .


2. Similarly, the domains and ranges of other inverse trigonometric functions are determined as


3. Similarly, the domains and ranges of other inverse trigonometric functions are determined as 


4. Similarly, the domains and ranges of other inverse trigonometric functions are determined as  


5. Similarly, the domains and ranges of other inverse trigonometric functions are determined as   


6. Similarly, the domains and ranges of other inverse trigonometric functions are determined as  


7. If  , then


8. If  , then


9. If  , then


10. If   ,then


11. If     then


12. If   then


13. If  , then 


14. If  then


15. If  then


16. If  then 


17. If   then


18. If , then


19. If  , then


20. If  then 


21. If  then


22. If    then  and


23. If    then   and


24. If    then   and


25. If  , then


26. If ,  then 


27. If  then


28. If  then


29. If , then


30. If   then


31. If  then


32. If  , then


33. If  then


34. If  , then


35.   for all


36. If  then


37. If  then


38. If  then


39. If 


40. For then and   if


41. If  then 


42. If  and


43. If 


44. If


45. If  then  and


46. If  , then


47. If  , then and if then


48.


49.


50.


51.


52. ,


53.


54.


55.


56.


57.


58. for all


59. for all


60. for all


61.


62.


for_INVERSE-TRIGONOMETRIC-FUNCTIONS