sin +

cos +

tan +

cot +

sec +

csc +

sin -

cos +

tan -

cot -

sec +

csc +

Degrees Radians !"#$ %&!$ '(#$ %&'$ !)%$ %!%$

0 *+,-.+ 0 1 0 -- 1 --

30/0

12

32

33

3 2 33

2

45/4

22

22

1 1 2 2

60/5

32

12

3 33

2 2 33

90/. 1 0 -- 0 -- 1

120./5

32

−12

− 3 −33

-2 2 33

1355/4

22

−22

-1 -1 − 2 2

1507/0

12 −

32

−33

− 3 −2 33

2

180 + 0 -1 0 -- -1 --

2108/0

−12 −

32

33

3 −2 33

-2

2257/4 −

22

−22

1 1 − 2 − 2

2404/5 −

32

−12

3 33

-2 −2 33

2705/.

-1 0 -- 0 -- -1

3007/5 −

32

12

− 3 −33

2 −2 33

3158/4 −

22

22

-1 -1 2 − 2

330 99/0

−12

32

−33

− 3 2 33

-2

Tangent and Cotangent Identities

tan= =sin=cos=

cot = =cos=sin=

Reciprocal Identities

csc= =1

sin=sin= =

1csc=

sec= =1

cos=cos= =

1sec=

cot = =1

tan=tan= =

1cot =

Pythagorean Identities

sinD = + cosD = = 1

tanD = + 1 = secD =

1 + cotD = = cscD =

Sum Formulas

sin F + G = sinF cosG + cosF sinG

cos F + G = cosF cosG − sinF sinG

tan F + G =tanF + tanG1− tanF tanG

Difference Formulas

sin F − G = sinF cosG − cosF sinG

cos F − G = cosF cosG + sinF sinG

tan F − G =tanF − tanG1+ tanF tanG

Half Angle Identities

sin=2= ±

1− cos=2

cos=2= ±

1+ cos=2

tan=2=1 − cos=sin=

=sin=

1 + cos=

Double Angle Identities

sin2= = 2sin= cos=

cos2= = cosD = − sinD =

cos2= = 2cosD = − 1

cos2= = 1 − 2sinD =

tan2= =2 tan=

1 − tanD=

TRIGONOMETRYDegrees to Radians

Formula

If x is an angle in degrees and t is an angle in radians,

then

IJKL

= MN

O = INJKL P = JKLM

I

Quad IQuad II

Quad IV

hyp

adj

opp

=Sakai-Kawada, F.

2018

sin +

cos -

tan -

cot -

sec -

csc +

sin -

cos -

tan +

cot +

sec -

csc - Quad III

Even and Odd Identities

sin −= = −sin =

cos −= = cos =

Cofunction Identities

sinQ2− = = cos=

cosQ2− = = sin=

Product to Sum Identities

cos R cos S =12cos R + S + cos R − S

sin R sin S =12cos R − S − cos R + S

sin R cos S =12sin R + S + sin R − S

RsinF

=S

sinG=

TsinU

RD = SD + TD − 2ST cosFSD = RD + TD − 2RT cosGTD = RD + SD − 2RS cosU

b a

cA

C

B

Law of Sines

Law of Cosines

NOTE: Trigonometric functions are periodic, in that they repeat

exactly in regular cycles.The length of the cycle is a called a

period

sin= =VWWℎYW = = sinZJ

VWWℎYW

cos= =R[\ℎYW

= = cosZJR[\ℎYW

tan= =VWWR[\ = = tanZJ

VWWR[\

Periodic Formulas

sin = + 2Q] = sin=

cos = + 2Q] = cos =

tan = + Q] = tan=