icon-komplexe-Zahl Contexts of trigonometric functions

Trigonometry

Trigonometry Angle, opposite cathetus Angle, adjacent cathetus Cathetus Cathetus, hypotenuse 2 sides, 1 angle 2 angles, 1 side 3 sides Tower height Cross bearing Triangle of forces Hansens task

Trigonometric functions

Tables Sine, Cosine, Tangent Power and n-th argument Triangle

Properties of trigonometric functions

Representation by other trigonometric functions

sin2x

cos2x

tan2x

cot2x

sin2x

-

1-cos2x

tan2x1+tan2x

11+cot2x

cos2x

1-sin2x

-

11+tan2x

cot2x1+cot2x

tan2x

sin2x1-sin2x

1-cos2xcos2x

-

1cot2x

cot2x

1-sin2xsin2x

cos2x1-cos2x

1tan2x

-

Function values of trigonometric functions

Radian

0

π6

π4

π3

π2

Degree

30°

45°

60°

90°

sin2x

0

12

122

123

1

cos2x

1

123

122

12

0

tan2x

0

133

1

3

-

cot2x

-

3

1

133

0

Reduction formulas (in degrees)

sin90°+x=cosx

cos90°+x=-sinx

tan90°+x=-cotx

cot90°+x=-tanx

sin180°+x=-sinx

cos180°+x=-cosx

tan180°+x=tanx

cot180°+x=cotx

Reduction formulas (in radians)

sinπ2+x=cosx

cosπ2+x=-sinx

tanπ2+x=-cotx

cotπ2+x=-tanx

sinπ+x=-sinx

cosπ+x=-cosx

tanπ+x=tanx

cotπ+x=cotx

Context of the trigonometric functions for the same argument

sinx2+cosx2=1

tanx=sinxcosx

cotx=cosxsinx=1tanx

cotxtanx=1

Addition theorems of trigonometric functions

sinx±y=sinxcosy±cosxsiny

cosx±y=cosxcosysinxsiny

tanx±y=tanx±tany1tanxtany

Addition theorems for multiples of the argument value

sin2x=2sinxcosx

sin3x=3sinx-4sin3x

cos2x=cos2x-sin2x

cos3x=4cos3x-3cosx

Half of the argument value

sinx2=±1-cosx2

cosx2=±1+cosx2

tanx2=±1-cosx1+cosx

Sum and difference of trigonometric functions

sinx+siny=2sinx+y2cosx-y2

cosx+cosy=2cosx+y2cosx-y2

sinx-siny=2cosx+y2sinx-y2

cosx-cosy=-2sinx+y2sinx-y2

cosx±sinx=2sinπ4±x=2cosπ4x

tanx±tany=sinx±ycosxcosy

cotx±coty=±sinx±ysinxsiny

tanx+coty=cosx-ycosxsiny

cotx-tany=cosx+ysinxcosy

Products of trigonometric functions

sinxsiny=12cosx-y-cosx+y

cosxcosy=12cosx-y+cosx+y

sinxcosy=12sinx-y+sinx+y

cosxsiny=12sinx+y-sinx-y

Potencies of trigonometric functions

sin2x=121-cos2x

sin3x=143sinx-sin3x

sinnx=12n k = 0 n n k cosn-2kx-π2

cos2x=121+cos2x

cos3x=143cosx+cos3x

cosnx=12n k = 0 n n k cosn-2kx