TRIGONOMETRY
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Trigonometric Identities
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sin(A+B) = sin(A) cos(B) + cos(A) sin(B)
sin(A-B) = sin(A) cos(B) - cos(A) sin(B)

cos(A+B) = cos(A) cos(B) - sin(A) sin(B)
cos(A-B) = cos(A) cos(B) + sin(A) sin(B)

sin^2(A) + cos^2(A) = 1

2 sin(A) cos(B) = sin(A+B) + sin(A-B)
2 cos(A) sin(B) = sin(A+B) - sin(A-B)
2 cos(A) cos(B) = cos(A+B) + cos(A-B)
2 sin(A) sin(B) = cos(A-B) - cos(A+B)

sin(2A) = 2 sin(A) cos(A)
cos(2A) = 1 - 2 sin^2(A)
tan(2A) = (2 tan(A)) / (1-tan^2(A))

sin(3A) = 3 sin(A) - 4 sin^3(A)
cos(3A) = 4 cos^3(A) - 3 cos(A)

sin A = 1/(csc A)
cos A = 1/(sec A)
tan A = 1/(cot A)

sin(-A) = - sin (A)
cos(-A) = - cos (A)

sin(A) / cos(A) = tan(A)
cos(A) / sin(A) = cot(A)

  sin(A) = cos(90-A)
  cos(A) = sin(90-A)
  sec(A) = cosec(90-A)
cosec(A) = sec(90-A)
  tan(A) = cos(90-A)
  cot(A) = tan(90-A)

sin(180-A) = sin(A)
cos(180-A) = -cos(A)
tan(180-A) = -tan(A)

1 + tan^2(A) = sec^2(A)
1 + cot^2(A) = cosec^2(A)

sin(A) + sin(B) = 2 sin((A+B)/2) cos((A-B)/2)
sin(A) - sin(B) = 2 cos((A+B)/2) sin((A-B)/2)
cos(A) + cos(B) = 2 cos((A+B)/2) cos((A-B)/2)
cos(A) - cos(B) = 2 sin((A+B)/2) sin((A-B)/2)

tan(A+B) = (tan(A) + tan(B)) / (1 - tan(A) tan(B))
tan(A-B) = (tan(A) - tan(B)) / (1 + tan(A) tan(B))



Triangles
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Cosine Law:       a^2 = b^2 + c^2 - 2 b c cos(A)

Sine Law:         sin(A)/a = sin(B)/b = sin(C)/c

Area of triangle: <area> = 0.5 b c sin(A) = 0.5 a c sin(B) = 0.5 a b sin(C)


Usefull values
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sin( 0) = 0
cos( 0) = 1
tan( 0) = 0

sin(45) = 1/sqrt(2)
cos(45) = 1/sqrt(2)
tan(45) = 1

sin(30) = 1/2
cos(30) = sqrt(3)/2
tan(30) = 1/sqrt(3)
cot(30) = sqrt(3)

sin(60) = sqrt(3)/2
cos(60) = 1/2
tan(60) = sqrt(3)
cot(60) = 1/sqrt(3)

sin(90) = 1
cos(90) = 0
tan(90) = undefined (infinite)



As usual, no guarentees are made as to the accuracy or obsolescence of this information.  Use at your own risk.