Then, sin y = 1
2 We know that the range of the principal value branch of sin–1 is 
−
2π π
,2
 and
sin 4
π





= 
1
2 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
−