Basic trigonometric identities Common angles

Basic trigonometric identities Common angles

Degrees 0 30 45 60 90

Radians 0

6

4

3

2

1

2

3

sin

0

1

2

2

2

3

2

1

cos

1

0

2

2

2

3

tan

0

1

3

3

Reciprocal functions Even/odd

1 cot x =

tan x 1

csc x = sin x 1

sec x = cos x

Pythagorean identities

sin(-x) = - sin x cos(-x) = cos x tan(-x) = - tan x

sin2 x + cos2 x = 1 1 + tan2 x = sec2 x 1 + cot2 x = csc2 x

1

Cofunction identities

sin( - x) = cos x

2 cos( - x) = sin x 2 tan( - x) = cot x 2 cot( - x) = tan x 2 sec( - x) = csc x 2 csc( - x) = sec x 2

Sum and difference of angles

Double angles

sin(x + y) = sin x cos y + cos x sin y sin(x - y) = sin x cos y - cos x sin y cos(x + y) = cos x cos y - sin x sin y cos(x - y) = cos x cos y + sin x sin y

tan x + tan y tan(x + y) =

1 - tan x tan y tan x - tan y tan(x - y) = 1 + tan x tan y

sin(2x) = 2 sin x cos x cos(2x) = cos2 x - sin2 x

= 2 cos2 x - 1 = 1 - 2 sin2 x

2 tan x tan(2x) = 1 - tan2 x

2

Half angles

Power reducing formulas

x

1 - cos x

sin = ?

2

2

x

1 + cos x

cos = ?

2

2

x 1 - cos x tan =

2 sin x

sin x =

1 + cos x

Product to sum

sin2 x = 1 - cos 2x 2

cos2 x = 1 + cos 2x 2

tan2 x = 1 - cos 2x 1 + cos 2x

1 sin x sin y = cos(x - y) - cos(x + y)

2 1 cos x cos y = cos(x - y) + cos(x + y) 2 1 sin x cos y = sin(x + y) + sin(x - y) 2 tan x + tan y tan x tan y = cot x + cot y tan x + cot y tan x cot y = cot x + tan y

3

Sum to product

x+y

x-y

sin x + sin y = 2 sin

cos

2

2

x+y

x-y

sin x - sin y = 2 cos

sin

2

2

x+y

x-y

cos x + cos y = 2 cos

cos

2

2

x+y

x-y

cos x - cos y = -2 sin

sin

2

2

sin(x + y) tan x + tan y =

cos x cos y

sin(x - y) tan x - tan y =

cos x cos y

Source

Basic triginometric identities by Evgenii Neumerzhitckii is licensed under a Creative Commons Attribution 4.0 International License.

4

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download