Trigonometry
Study Guide
Sec. 6.1
Name __________________________________________________
Date ____________________________________ Period ______
Inverse Circular Functions
y
Horizontal Line Test
Any horizontal line will intersect the graph of a __________________________________ function
in at most
one point.
x
The ________________________________ function of the one-to-one function f is
defined as f -1 = {______________________________________________}
Inverse Functions Review
1. In a one-to-one function, each ____-value corresponds to only one ____-value and each ____-value
corresponds to only one ____-value.
2. If a function f is one-to-one, then f has an ____________________ function f -1.
3. The domain of f is the _____________________ of f -1and the _______________________ of f is the domain of f -1.
4. The graphs of f and f -1 are ____________________________ of each other about the line ________________________.
5. To find f -1(x) from f (x), follow these steps.

Replace f (x) with ___________and ___________________________________ x and y.

Solve for ____________.

Replace _____________ with f -1 (x).
Inverse Sine Function
𝜋
𝜋
y = sin -1 x or y = arc sin x means that ________________________________________, for − ≤ 𝑦 ≤ .
2
Example 1:
1
a) Find y = arcsin (− )
2
b) sin -1
√3
2
c) sin -1 2
2
Inverse Sine Function

The inverse sine function is ______________________________and _________________________________on its domain
[-1, 1].

Its x-intercept is _______, and its y-intercept is _______.

Its graph is symmetric with respect to the _____________________; it is an _______________ function.
Inverse Cosine Function
y = cos -1 x or y = arccos x means that x = cos y, for 0 ≤ y ≤ π.
Example 2: Find arccos
√2
2
Inverse Cosine Function

The inverse cosine function is ______________________________and _________________________________on its
domain [-1, 1].

Its x-intercept is _______, and its y-intercept is _______.

Its graph is not symmetric with respect to the _____________________ or the __________________________.
2
Inverse Tangent Function
𝜋
𝜋
y = tan -1 x or y = arc tan x means that x = tan y, for − ≤ 𝑦 ≤ .
2

2
The inverse tangent function is ______________________________and _________________________________on its
domain [-∞, ∞].

Its x-intercept is _______, and its y-intercept is _______.

Its graph is symmetric with respect to the _____________________; it is an _______________ function.

The lines y = _________ and y = __________ are horizontal ___________________________________.
Other Inverse Functions
Inverse Function
Domain
Interval
Example 3:
Find the degree measure of θ in the following:
a) θ = arctan 1
Range
Quadrants of the Circle
b) θ = sec -1 2
3
Example 4:
a) Find y in radians if y = arctan (-6.24).
b) Find y in radians if y = arccos 2.
Example 5:
3
Evaluate the expression without using a calculator. 𝑠𝑖𝑛 (𝑡𝑎𝑛 −1 2)
Example: Evaluate the expression without using a calculator.
Example 6:
2
Evaluate the expression 𝑡𝑎𝑛 (2 𝑎𝑟𝑐𝑠𝑖𝑛 5) without using a calculator.
Homework:
pp. 246-249, 1-6 all, 8, 14-52 even, 58-62 all, 64-78 even, 79-82 all, & 84-96 even.
4