formule trigonometriche (PDF)




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Author: Raffaele SANTORO

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Formule di Trigonometria
sin 2   cos2   1

cos   





0
30


0


6

4

3

2

45
60
90

1
1  tan2 





sin   









sin
0
1
2

1

1

1

0



1  cos
2



1  cos
cos  
2
2
 1  cos

 1  cos
  1  cos
tan  
2  sin 
 sin 
 1  cos
Formule di triplicazione

sin3  3sin  4 sin3 
cos3  4 cos3   3cos





2
2
3
2

2 tan 
1  tan 2 
Formule di bisezione

2



cot


tan 2 



1  tan2 

tan
0
3
3

cos2   sin 2 

cos 2  2 cos2   1

2
1  2 sin 



tan 

cos
1
3
2
2
2
1
2

Formule di duplicazione
sin 2  2 sin  cos

sin

cos    1  sin2 

sin    1  cos2 



Formule di addizione
cos(  )  cos  cos   sin  sin 
cos(  )  cos  cos   sin  sin 

sin(  )  sin  cos   sin  cos 
sin(  )  sin  cos   sin  cos 

3

tan   tan 
1  tan  tan 
tan   tan 
tan(  ) 
1  tan  tan 
tan(  ) 

3
3

3



0

Formule parametriche
2t 
sin  
1 t 2 
1  t 2  

 t  tan 
cos 
2
2
1 t  
2t 
tan  
1  t 2 

Formule di prostaferesi
pq
pq
sin p  sin q  2 sin
cos
2
2
pq
pq
sin p  sin q  2 sin
cos
2
2
pq
pq
cos p  cos q  2 cos
cos
2
2
pq
pq
cos p  cos q  2 sin
sin
2
2

Triangoli rettangoli
C

A



c

a

b
A

Triangoli qualunque


c

B

b  a sin   a cos  c tan 
b
b
b
a

; tan  
sin  cos 
c
c  a sin   a cos   b tan 
c
c
c
a

; tan  
sin  cos 
b

B

b






a

C

a
b
c


sin  sin  sin 

a 2  b 2  c 2  2bc cos
b 2  a 2  c 2  2ac cos 
c 2  a 2  b 2  2ab cos 
1
Area (ABC)  bc sin 
2
1
 ac sin 
2
1
 ab sin 
2






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