Math Formulas: Trigonometry Identities



Math Formulas: Trigonometry Identities

Right-Triangle Definitions

Opposite

1.

sin =

Hypotenuse

Adjacent

2.

cos =

Hypotenuse

Opposite

3.

tan =

Adjacent

1 Hypotenuse

4.

csc =

=

sin Opposite

1 Hypotenuse

5.

sec =

=

cos Adjacent

1 Adjacent

6.

cot =

=

tan Opposite

Reduction Formulas

7.

sin(-x) = - sin(x)

8.

cos(-x) = cos(x)

9.

sin - x = cos(x)

2

10.

cos - x = sin(x)

2

11.

sin + x = cos(x)

2

12.

cos + x = - sin(x)

2

13.

sin( - x) = sin(x)

14.

cos( - x) = - cos(x)

15.

sin( + x) = - sin(x)

16.

cos( + x) = - cos(x)

Basic Identities

17.

sin2 x + cos2 x = 1

18.

tan2

x

+

1

=

1 cos2

x

19.

cot2

x

+

1

=

1 sin2

x

Sum and Difference Formulas

1

20.

sin( + ) = sin ? cos + sin ? cos

21.

sin( - ) = sin ? cos - sin ? cos

22.

cos( + ) = cos ? cos - sin ? cos

23.

cos( - ) = cos ? cos + sin ? cos

tan + tan

24.

tan( + ) =

1 - tan ? tan

tan - tan

25.

tan( - ) =

1 + tan ? tan

Double Angle and Half Angle Formulas

26.

sin(2 ) = 2 ? sin ? cos

27.

cos(2 ) = cos2 - sin2

2 tan

28.

tan(2 ) = 1 - tan2

1 - cos

29.

sin = ?

2

2

1 + cos

30.

cos = ?

2

2

1 - cos sin

31.

tan =

=

2 sin 1 - cos

1 + cos

32.

tan = ?

2

1 - cos

Other Useful Trig Formulas

Law of sines 33. Law of cosines

34.

sin sin sin

=

=

a2 = b2 + c2 - 2 ? b ? c ? cos b2 = a2 + c2 - 2 ? a ? c ? cos c2 = a2 + b2 - 2 ? a ? b ? cos

Area of triangle 35.

1 A = a b sin

2



2

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