Trigonometry

sin 30°

1/2

sin 45°

1/√2

sin 60°

√3/ 2

cos 30°

√3/ 2

cos 45°

1/√2

cos 60°

1/2

tan 30°

1/√3

tan 45°

1

tan 60°

√3

pythagorean identities (list all)

𝝅

180°

𝝅/2

90°

𝝅/3

60°

𝝅/4

45°

𝝅/6

30°

sin 90°

1

cos 90°

0

tan 90°

undefined

sin 𝝅/2

1

sin 𝝅/6

1/2

sin 𝝅/4

√2/ 2

sin 𝝅/3

√3/ 2

cos 𝝅/2

0

cos 𝝅/6

√3/ 2

cos 𝝅/4

√2/ 2

cos 𝝅/3

1/2

tan 𝝅/2

undefined

tan 𝝅/6

1/√3

tan 𝝅/4

1

tan 𝝅/3

√3

csc 𝜃

1 / sin 𝜃

sec 𝜃

1 / cos 𝜃

cot 𝜃

1 / tan 𝜃

sin 𝜃

opp / hyp

cos 𝜃

adj / hyp

tan 𝜃

opp / adj

Law of Sines

Law of Cosines

y = sin x (graph)

y = cos x (graph)

y = tan x (graph)

y = csc x (graph)

y = sec x (graph)

y = cot x (graph)

sin² 𝜃 + cos² 𝜃 =

1

sec² 𝜃 - tan² 𝜃 =

1

csc² 𝜃 - cot² 𝜃 =

1

sin (90 - 𝜃) =

cos 𝜃

cos (90 - 𝜃) =

sin 𝜃

tan (90 - 𝜃) =

cot 𝜃

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 + y) =

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

tan (x - y) =

(tan x - tan 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

tan (2x) =

(2 tan x)/(1 - tan² x)

sin² x =

(1 - cos(2x) )/2

cos² x =

(1 + cos(2x) )/2

sin 0°

0

cos 0°

1

tan 0°

0

triangle area formula

1/2 ABsin(c)

cos rule for side

c^2 = a^ + b^2 - 2ab cos(c)

cos rule for angle

cos C = (a^2 +b^2 - c^2)/2ab