## Inverse Trigonometry

### 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