Download Lesson 14 Inverse Functions

WARM UP
 A man on a 135-ft vertical cliff looks
down at an angle of 16 degrees and
sees his friend. How far away is the
man from his friend? How far is the
friend from the base of the cliff?
LESSON 14 INVERSE FUNCTIONS
Objective: To introduce inverse
functions and use them to find the
angles of right triangles.
INVERSE FUNCTIONS
 Inverse functions sin-1 or arcsin

cos-1 or arccos

tan-1 or arctan
 They are used to find the missing angle
in a right triangle.
 THESE ARE NOT THE SAME AS THE
RECIPROCAL OF THE FUNCTION

1
Sin-1 x =
sin x
FINDING THE ANGLE
 To find the angle β– use one of the trig
functions that you have the info for.
4
Ex: sin β =
5
β
because we
5
3
don’t know the
angle.

α
C
4
A
Press [2nd] [sin-1] (4/5)
This will give you the
Degrees of angle β
 3

cos 

2


1
EXAMPLES
30o

3

cos  

2


150o
 1
sin 1   
 2
-30o
tan 1 1
45o
1
WARM UP
 Find the angle – round to the nearest
degree:
 Sin A = .9063
 Cos B = .6428
 Tan C = .4040
USING THE UNIT CIRCLE
 Inverse functions can be evaluated
using the unit circle.
 Only the angles between -90 and 90
are used.
3
-1
 Ex: sin ( ) could be either 60o or
2
o
120 , so we are taking the one that is
less than 90o
FIND THE ANGLES USING THE UNIT
CIRCLE
 3

sin 

2


60o
tan 1 1
45o
1
 2

cos 

2


1
45o

COMBINING FUNCTIONS WITH
INVERSES
 2  means that you
)
tan(cos 

2


1
want to find the tangent of whatever
angle has a cosine of 2
2
We are only going to do this on the
calculator.
 2
)  1
tan(cos 

2


1
PRACTICE
 Cos(tan-1(.95)) =
 .725
 Sin(cos-1(5/6))=
 .5528
 Tan(tan-1(2) =
 2