Download Trigonometry Definition of the Trigonometric Functions Right triangle definitions, where

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Trigonometry
Definition of the Trigonometric Functions
Right triangle definitions, where 0   

2
opp
hyp
sin 
.
hyp
opp
hyp
sec  
adj
adj
cot  
opp
csc  
adj
hyp
opp
tan 
adj
cos  
Circular function definitions, where θ is any angle.
y
r
x
cos  
r
y
tan 
x
sin 
(x,y)
y
r
θ
x
r
y
r
sec  
x
x
cot  
y
csc  
Special Right Triangles
Reciprocal Identities
1
csc x
1
csc x 
sin x
sin x 
1
sin x

cot x cos x
1
cos x
cot x 

tan x sin x
1
sec x
1
sec x 
cos x
cos x 
tan x 
1  cos 2
2
1  cos 2
2
tan  
1  cos 2
sin2  
Pythagorean Identities
sin2 x  cos 2 x  1
1  tan2 x  sec 2 x
Power Reducing Formulas
1  cot 2 x  csc 2 x
cos 2  
1  cos 2
2
Half-Angle Formulas
Cofunction Identities



1  cos 
2

1  cos  1  cos 
sin


1  cos 
sin
1  cos 
1  cos 
2


sin  x   cos x
2



cos   x   sin x
2

sin


csc   x   sec x
2



tan  x   cot x
2

tan


sec  x   csc x
2



cot   x   tan x
2

Product-to-Sum Formulas
Sum-to-Product Formulas
1
sin sin   cos      cos    
2
csc x    csc x
cot x    cot x
cos  cos  
1
cos      cos    
2
      
sin  sin   2 sin
 cos 
 2   2
      
sin  sin   2 cos 
 sin
 2   2
sin cos  
1
sin     sin   
2
cos  sin  
1
sin     sin   
2
Odd Identities
sinx    sin x
tanx    tanx
Even Identities
cos x   cos x
secx   sec x
2

2
cos
2







      
cos   cos   2 cos 
 cos 

 2   2 
       
cos   cos   2 sin
 sin

 2   2 
Sum and Difference Formulas
sin     sin cos   cos  sin 
cos      cos  cos   sin sin 
tan  tan
tan    
1  tan tan
Double-Angle Formulas
sin2  2 sin cos 
cos 2  cos 2   sin2   2 cos 2   1  1  2 sin2 
2 tan
tan2 
1  tan2 
Law of Sines
a
b
c


sin A sin B sin C
Area of Oblique Triangle
1
1
1
Area  bc sin A  ab sinC  ac sin B
2
2
2
Law of Cosines
b2  a2  c 2  2ac cos B
2
2
a2  b2  c 2  2bc cos A
2
c  a  b  2ab cos C
Heron’s Formula for the Area of a Triangle
Area  ss - as  bs  c  where s 
1
a  b  c 
2
Zabrocki 2014
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