GSE Pre-Calculus and (Honors)
Principal Values of the Inverse Trigonometric Functions
The inverse trigonometric functions are basically the reverse of the given trigonometric functions.
These are: sin -1 x, cos -1 x , tan -1 x , csc -1 x , sec -1 x , cot -1 x (we will NOT study the last three).
Principal value is the set of all values that a function will take for different values of x. The set of all x values is
called the domain. The range of the inverse trigonometric functions always lies between certain values, it does
not go to infinity. Here we consider the domain from -1 to 1. Let’s review what we know about the domain and
ranges from our inverse functions studied over the past few days…
Principal Values of the Inverse Trigonometric Functions Table
Function
Domain
y = sin-1 x
[- 1, 1]
y=
cos-1x
[- 1, 1]
y=
tan-1x
R
Principal Value (Range)
[[0,
,
(-
,
]
]
)
Examples on Principal Values
Example 1:
1
Calculate the principal value for the inverse function Sin−1 (2). (How I read this statement is the
following, “_____________________________________________________________________).
Example 2:
Calculate the principal value for the inverse function Arctan−1 √3.
Practice Problems
Problem 1:
Calculate the principal value for the inverse function Sin-1
.
Problem 2:
Calculate the principal value for the inverse function Arccos-1
.