Therefore, principal value of sin–1 
1
2





  is 4
π
Example 2 Find the principal value of cot–1 
1
3
−





Solution Let cot–1 
1
3
−





 = y Then,
1
cot
cot 3
3
y
−
π

=
= −



 = cot
π3


π −


  = 
cot2
π3





We know that the range of principal value branch of cot–1 is (0, π) and
cot 2
π3





= 
1
3
− Hence, principal value of cot–1 
1
3
−




  is 2
3
π
EXERCISE 2 1
Find the principal values of the following:
1