TrigonometricFunctions/Trigonometric Identities
The following is a (partial) list of trigonometric identities:
- sin(x) = sin(x + 2π)
- cos(x) = cos(x + 2π)
- sin(x) = cos(x - π/2)
- sin(-x) = -sin(x)
- cos(-x) = cos(x)
- sin2x + cos2x = 1
- sin2x + sin2(x+π/2) = 1
- sin4x + sin4(x+π/4) + sin4(x+π/2) + sin4(x+3 π/4) = 3/2
- sin6x + sin6(x+π/4) + sin6(x+π/2) + sin6(x+3 π/4) = 5/4
- cos(x+y) = cos(x) cos(y) - sin(x) sin(y)
- sin(x+y) = sin(x) cos(y) + cos(x) sin(y)
- cos(2x) = 2 cos2x - 1 = 1 - 2sin2x
- sin(2x) = 2 sin(x) cos(x)
- sin(x/2) = sqrt((1-cos(x)) / 2)
- cos(x/2) = sqrt((1+cos(x)) / 2)
- sin(x) + sin(y) = 2 sin((x+y) / 2) cos((x-y) / 2)
- cos(x) + cos(y) = 2 cos((x+y) / 2) cos((x-y) / 2)
- 2 cos(x) cos(y) = cos(x+y) + cos(x-y)
- -2 sin(x) sin(y) = cos(x+y) - cos(x-y)
- 2 sin(x) cos(y) = sin(x+y) + sin(x-y)
- tan(x) = sin(x) / cos(x)
- cot(x) = cos(x) / sin(x)
- tan(x) = tan(x + π)
- cot(x) = cot(x + π)
- cot(x) = tan(π/2 - x)
- d/dx sin(x) = cos(x)
- d/dx cos(x) = -sin(x)
- d/dx arctan(x) = 1 / (1 + x2)
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