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