Suppose we are given
cos ^{ -1 } (1/2)
Β
Principal value of cos ^{ -1 } (1/2) means
the angle x where cos xΒ = 1/2
Β
We use this table for our help
Β |
Range |
Positive |
Negative |
sin ^{ -1 } |
[-Ο/2, Ο/2] |
ΞΈ |
Β β ΞΈ |
cos ^{ -1 } |
[0,Ο] |
ΞΈ |
Β Ο β ΞΈ |
tan ^{ -1 } |
(-Ο/2, Ο/2) |
ΞΈ |
Β β ΞΈ |
Β
And we follow these steps
- Put y = cos ^{ -1 } (1/2)
- So, cos y = 1/2
- Now ignore the signs and find value ofΒ ΞΈ
- Using the table, Find principal value according to the table
Β
Let's look at some examples
Find the principal value of cos ^{ β1 } ( 1/2 )
Find the principal value of cos ^{ β1 } (-1 /2 )
Find the principal value of sin ^{ β1 } ( 1/2 )
Find the principal value of sin ^{ β1 } (-1/2)
Find the principal value of tan ^{ β1 } (1)
Find the principal value of tan ^{ β1 } (-1 )