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4.3 Right Triangle
Trigonometry
Trigonometric Identities
The part of a Right Triangle with
respect to an angle
Adjacent, Opposite and Hypotenuse.
hypotenuse
opposite

adjacent
Trig functions defined using the
parts of the right triangle
Sine, Cosine, Tangent, Cosecant, Secant
and Cotangent
opposite
Sin  
hypotenuse
adjacent
Cos 
hypotenuse
opposite
Tan 
adjacent
hypotenuse
Csc 
opposite
hypotenuse
Sec 
adjacent
adjacent
Cot 
opposite
Sin 60º = Cos 30º
If

< 90º
Sin 90     Cos
Cos90     Sin
Tan90     Cot
Cot 90     Tan
Sec90     Csc
Csc90     Sec
Sin 90     Cos
Cos90     Sin 
Tan90     Cot
Cot 90     Tan
Sec 90     Csc
Csc 90     Sec
Sin 42º= Cos(90º - 42º) = Cos 48º
Trigonometric Identities
Some basic identities
1
1
1
Sin 
 Cos 
Tan 
Csc
Sec
Cot
Sin
Cos
Tan 
 Cot 
Cos
Sin
Trigonometric Identities
Very important identity
sin   cos   1
2
2
And the identities that you can find
1  tan 2   sec 2 
1  cot 2   csc 2 
Angle of elevation or
Angle of depression
Angle of elevation:
the angle it rise from horizontal
Angle of depression:
the angle it drops from horizontal
What is the Angle of elevation
Find 
2miles

8miles
Find 
6 ft
2.5 ft

Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
sin 2 
cos 2 


sin  cos  sin  cos 
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
sin 2 
cos 2 


sin  cos  sin  cos 
sin 2   cos 2 

sin  cos 
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
sin 2 
cos 2 


sin  cos  sin  cos 
sin 2   cos 2 

sin  cos 
1

sin  cos 
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
sin 2 
cos 2 


sin  cos  sin  cos 
sin 2   cos 2 

sin  cos 
1

sin  cos 
1
1


sin  cos 
Prove a Trigonometric Identity
Work only on one side
tan   cot   csc sec
sin  cos 


cos  sin 
sin 2 
cos 2 


sin  cos  sin  cos 
sin 2   cos 2 

sin  cos 
1

sin  cos 
1
1


sin  cos 
csc sec  csc sec
Homework
Page 287- 290
# 3, 9, 15, 18,
21, 25, 31, 36,
40, 46, 48, 51,
55, 57, 61, 66,
71, 74, 82, 86
Homework
Page 287- 290
# 6, 12, 17, 20,
24, 28, 34, 37,
44, 47, 50 54,
56, 60, 65, 68,
72, 75, 84
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