Trigonometric Identities

cos(A-B) =

(cosA * cosB) + (sinA * sinB)

sin(A-B) =

(sinA * cosB) - (cosA * sinB)

tan(A-B) =

(tanA - tanB) / (1 + (tanA * tanB))

cos(-Φ) =

-cosΦ

sin(-Φ) =

-sinΦ

tan(-Φ) =

-tanΦ

cos^2Φ + sin^2Φ =

1

secΦ =

1/cosΦ

cscΦ =

1/sinΦ

cotΦ =

1/tanΦ

Law of Cosines, for a

a^2 = b^2 + c^2 - 2bc * cosA

Law of Cosines, for b

b^2 = a^2 + c^2 - 2ac * cosB

Law of Cosines, for c

c^2 = a^2 + b^2 - 2ab * cosC

sin(π/2 - Φ) =

cosΦ

cotΦ =

cosΦ/sinΦ

tan(π/2 - Φ) =

cot(Φ)

1 + cot^2Φ =

csc^2Φ

secΦ

r/x = H/A

cscΦ

r/y = H/O

1 + tan^2Φ =

sec^2Φ

Law of Sines

sin A/a = sin B/b = sin C/c

tanΦ =

sinΦ/cosΦ

cosΦ

x/r = A/H

cotΦ

x/y = A/O

sinΦ

y/r = O/H

tanΦ

y/x = O/A