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Inverse Trig Functions
Law of the Sines
1
2
3
Notation
Inverse Trig Functions, Law of the
Sines & Requirements
Practice Problems
Notation
2

New variables for angles
 Alpha
 Beta



 Gamma
 Theta

Inverse Trig Functions
3

Arcsine
 sin-1

Arc-cosine
 cos-1

Arctangent
 tan-1
Inverse Trig Functions(Cont.)
4

Reverse the trig function process, where:
opp
sin  
hyp
adj
cos  
hyp
opp
tan  
adj
the arc functions provide for:
 opp 
  
sin 
 hyp 
1
1  adj 
  
cos 
 hyp 
 opp 
  
tan 
 adj 
1
Inverse Trig Functions Example
5

Solve
sin  
3
2
to the nearest degree:
3
sin  
2
 3
sin 
  
 2 
1
60  
Area of a Triangle
6
1
area  bc sin 
2
1
area  ac sin 
2
1
area  ab sin 
2
Area of a Triangle Example
7

Find the area of the triangle given B=85˚, c=23 ft.,
and a=50 ft. to the nearest tenth.
1
area  ac sin B
2
1
area  (50 ft.)(23 ft.) sin 85
2
area  572.8 ft
2
Law of the Sines
8
Law of the Sines
9

Requirements
 Two
sides and an angle opposite to one of them
 SSA
 Two
angles and any side
 AAS
 If
or ASA
these conditions are not met, the problem cannot be
solved with the Law of the Sines
Example
10
  180  57  48  75
sin  sin 

a
b
sin 48 sin 75

a
47
47sin 48
a
sin 75
 36.2
Example (Cont.)
11
sin  sin 

c
b
sin 57 sin 75

c
47
47 sin 57
c
sin 75
 40.8
Tips
12

Check your calculator settings
 Make
sure you are in degree mode when working with
degrees and in radian mode when working with
radians!!!!


Remember the sum of all angles in a triangle is 180
degrees or pi radians
Not all problems can be solved with the Law of
Sines