Suppose we are given
cos ^{ 1 } (1/2)
Principal value of cos ^{ 1 } (1/2) means
the angle x where cos x = 1/2
We use this table for our help
Range 
Positive 
Negative 

sin ^{ 1 } 
[π/2, π/2] 
θ 
– θ 
cos ^{ 1 } 
[0,π] 
θ 
π – θ 
tan ^{ 1 } 
(π/2, π/2) 
θ 
– θ 
And we follow these steps
 Put y = cos ^{ 1 } (1/2)
 So, cos y = 1/2
 Now ignore the signs and find value of θ
 Using the table, Find principal value according to the table
Let's look at some examples
Find the principal value of cos ^{ –1 } ( 1/2 )
Find the principal value of cos ^{ –1 } (1 /2 )
Find the principal value of sin ^{ –1 } ( 1/2 )
Find the principal value of sin ^{ –1 } (1/2)
Find the principal value of tan ^{ –1 } (1)
Find the principal value of tan ^{ –1 } (1 )