Trigonometric Identities
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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
