trigonometry formula sheet math 141/142 fundamental identities: tan  =

sin  cos 

cot  =

cos  sin 

csc  =

1 sin 

sec  =

1 cos 

pythagorean identities: sin2  + cos2  = 1

tan2  + 1 = sec2 

cot2  + 1 = csc2 

even/odd identities: cos( sin( tan(

) = cos  ) = sin  ) = tan 

) = sec  ) = csc  ) = cot 

sec( csc( cot(

double angle formulas: sin(2) = 2 sin  cos 

cos(2) = cos2  sin2  = 2 cos2  2 tan  tan(2) = 1 tan2 

1=1

2 sin2 

half angle formulas:  

sin



2

r

=

cos  2

1

 

cos



2

r

=

1 + cos  2

 

tan



2

=

1

cos  sin 

sum and difference formulas: sin(  ) = sin  cos  cos  sin cos(  ) = cos  cos  sin  sin tan   tan tan(  ) = 1  tan  tan confunction identities: sin csc tan



2  2  2



 = cos 

cos

 = sec 

sec

 = cot 

cot

 



2  2  2



 = sin  

 = csc  

 = tan 

product to sum identities:
1 cos( ) cos( + ) 2
1 = cos( ) + cos( + ) 2
1 = sin( + ) + sin( ) 2

sin 
sin = cos 
cos sin 
cos

1

trigonometry formula sheet math 141/142

sum to product identities: sin   sin = 2 sin cos  + cos = 2 cos cos 

cos =

 2

+ 2

2 sin

cos

+ 2



cos

2



sin

2

 2

law of sines and law of cosines: in a triangle with angle  opposite side of length a , angle opposite side of length b , and angle opposite side of length c the following identities hold: sin  sin sin = = a b c a 2 = b 2 + c 2 2bc cos  b2 = a2 + c2 2

2

c =a +b

2

2ac cos 2ab cos

2