May 18, 2017
Warm-up
State all angles such that 0 < x < 2
for which the statement is true.
cos x = -1/2
sin x =
tan x = -1
tan x = - 3
4.7 Inverse Trig Functions
Objectives:
To understand the domains and ranges of
inverse sine, cosine and tangent
To evaluate inverse trig functions.
May 18, 2017
Notation for inverse trig functions:
y = sin-1x or y = arcsin x
y = cos-1x or y = arccos x
y = tan-1x or y = arctan x
Evaluate:
y = sin-1(
)
Does y = sin x have an inverse that is a function?
How do you know?
We can restrict the domain of the sine function in order to
define the inverse function. Which part of the sine
function would you use?
May 18, 2017
sin
ou
e
tp
u
va
lu
y = sin-1x
t
e
y = sinx
m
an
ea
y = arcsin x
inp
gle
su
ut
re
ou
a
t is
tpu
gle
an
n
-1
y = sin x
y = sinx does not have an inverse function.
We can restrict the domain so that the
inverse will be a function.
R:
Evaluate:
sin-1 (1/2) =
sin-1 (-1/2) =
sin-1 (- √32 ) =
sin
inp
e
ut
va
is
lue
a
May 18, 2017
y = cos x
Which part would you use to define the inverse
function?
y = cos-1x
cosine
value
y = cos x
y = arccos x
angle
angle
measure
measure
-1
y = cos x
a cosine
value
May 18, 2017
Evaluate:
cos-1
May 18, 2017
y = tan-1x
y = tan x
Evaluate:
tan-1 (tan-1 (
)
)
y = arctan x
y = tan-1x
May 18, 2017
D:
D:
D:
R:
R:
R:
Evaluate:
1.)
6.)
2.)
7.)
3.)
8.)
4.)
9.)
5.)
10.)
May 18, 2017
Evaluate:
1.)
6.)
2.)
7.)
3.)
8.)
=0
4.)
9.)
=0
5.)
10.)
May 18, 2017
Evaluate:
1.)
6.)
2.)
7.)
3.)
4.)
5.)
May 18, 2017