Name ____________________________________Date ______________Block _____
Adv. Math: Chapter 6
Lesson 8: Trigonometric Inverses and
Their Graphs
Objectives:
 Graph inverse trigonometric functions
 Find principal values of inverse trigonometric functions
**Find the inverse of y = 3x – 10
**What happens to the domain and the range????
**Is the inverse of every function also a function????
**What line are they
Reflected over????
**What test can we use on the function to see if its inverse is also a function?????
Relation
Ordered
Pairs
y = sin x
(x, sin x)
Graph
Domain
Range
all real
numbers
-1 ≤ x ≤1
Domain
Range
all real
numbers
-1 ≤ x ≤1
y = arcsin x
Relation
Ordered
Pairs
y = cos x
(x, cos x)
y = arccos x
Graph
Relation
y = tan x
Ordered
Pairs
(x, tan x)
Graph
Domain
Range
all real #s
except π/2n,
(n → odd)
all real
numbers
y = arctan x
Principal Values -
Ex. 1:
a) Write the equation for the inverse of y = Arctan 2x. Then graph the function and
its inverse.
b) Write the equation for the inverse of y = Arcsin x. Then graph the function and
its inverse.
Ex. 2: Find each value.
a) Arcsin (−
√𝟐
)
𝟐
c) sin (Tan-1 1 - Sin-1 1)
Homework:
b)
𝝅
Sin-1 (cos )
𝟐
d) cos [Cos-1 (−
√𝟐
)
𝟐
𝝅
− ]
𝟐