Mathc initiation/a78a
Sommaire ◀ Utilise la commande "Retour en Arrière" de ton navigateur.
| Trigonométriques | Trigonométriques hyperboliques |
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* cos(x)**2 + sin(x)**2 = 1
* sec(x)**2 - tan(x)**2 = 1
* csc(x)**2 - cot(x)**2 = 1
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sin(x+y) = cos(x) sin(y) + sin(x) cos(y)
cos(x+y) = cos(x) cos(y) - sin(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)
tan(x+y) = (tan(x)+tan(y)) / (1-tan(x)*tan(y))
tan(x-y) = (tan(x)-tan(y)) / (1+tan(x)*tan(y))
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cos(2x) = cos(x)**2 - sin(x)**2
= 1 - 2sin(x)**2
= 2cos(x)**2 - 1
cos(3x) = 4cos(x)**3 - 3cos(x)
cos(4x) = 8cos(x)**4 - 8cos(x)**2 + 1
sin(2x) = 2cos(x) sin(x)
sin(3x) = 3sin(x) - 4sin(x)**3
sin(4x) = 4sin(x) cos(x) - 8sin(x)**3 cos(x)
tan(2x) = (2*tan(x)) / (1- tan(x)**2)
tan(3x) = (3tan(x)-tan(x)**3) / (1-3tan(x)**2)
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cos(x)**2 = 1/2 + 1/2 cos(2x)
cos(x)**3 = 3/4 cos(x) + 1/4 cos(3x)
cos(x)**4 = 3/8 + 1/2 cos(2x) + 1/8 cos(4x)
sin(x)**2 = 1/2 - 1/2 cos(2x)
sin(x)**3 = 3/4 sin(x) - 1/4 sin(3x)
sin(x)**4 = 3/8 - 1/2 cos(2x) + 1/8 cos(4x)
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sin(x/2) = sqrt( (1-cos(x))/2)
cos(x/2) = sqrt( (1+cos(x))/2)
tan(x/2) = sqrt( (1-cos(x)) / (1+cos(x)) )
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sin(x)sin(y) = 1/2 [cos(x-y) - cos(x+y)]
cos(x)cos(y) = 1/2 [cos(x-y) + cos(x+y)]
sin(x)cos(y) = 1/2 [sin(x-y) + sin(x+y)]
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sin(x) + sin(y) = 2 sin((x+y)/2) cos((x-y)/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)
cos(x) - cos(y) = -2 sin((x+y)/2) sin((x-y)/2)
= 2 sin((x+y)/2) sin((y-x)/2)
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sin(acos(x)) = sqrt(1-x**2)
cos(asin(x)) = sqrt(1-x**2)
sec(atan(x)) = sqrt(1+x**2)
csc(acot(x)) = sqrt(1+x**2)
tan(asec(x)) = sqrt(x**2-1)
cot(acsc(x)) = sqrt(x**2-1)
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* cosh(x)**2 - sinh(x)**2 = 1
* sech(x)**2 + tanh(x)**2 = 1
* coth(x)**2 - csch(x)**2 = 1
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sinh(x+y) = cosh(x) sinh(y) + sinh(x) cosh(y)
cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y)
sinh(x-y) = sinh(x) cosh(y) - cosh(x) sinh(y)
cosh(x-y) = cosh(x) cosh(y) - sinh(x) sinh(y)
tanh(x+y) = [tanh(x)+tanh(y)] / [1+tanh(x)*tanh(y)]
tanh(x-y) = [tanh(x)-tanh(y)] / [1-tanh(x)*tanh(y)]
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cosh(2x) = cosh(x)**2 + sinh(x)**2
= 1 + 2*sinh(x)**2
= 2*cosh(x)**2 - 1
cosh(3x) = 4*cosh(x)**3 - 3*cosh(x)
cosh(4x) = 8 cosh(x)**4 - 8 cosh(x)**2 + 1
sinh(2x) = 2 cosh(x) sinh(x)
sinh(3x) = 3 sinh(x) + 4*sinh(x)**3
sinh(4x) = 4 cosh(x) sinh(x) + 8 sinh(x)**3 cosh(x)
tanh(2x) = (2 tanh(x))/(1 + tanh(x)**2)
tanh(3x) = (3 tanh(x) + tanh(x)**3) / (1+3 tan(x)**2)
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cosh(x)**2 = 1/2 + 1/2 cosh(2x)
cosh(x)**3 = 3/4 cosh(x) + 1/4 cosh(3x)
cosh(x)**4 = 3/8 + 1/2 cosh(2x) + 1/8 cosh(4x)
sinh(x)**2 = 1/2 cosh(2x) - 1/2
sinh(x)**3 = 1/4 sinh(3x) - 3/4 sinh(x)
sinh(x)**4 = 3/8 - 1/2 cosh(2x) + 1/8 cosh(4x)
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sinh(x) sinh(y) = 1/2 [cosh(x+y) - cosh(x-y)]
cosh(x) cosh(y) = 1/2 [cosh(x-y) + cosh(x+y)]
sinh(x) cosh(y) = 1/2 [sinh(x-y) + sinh(x+y)]
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sinh(x) + sinh(y) = 2 sinh((x+y)/2) cosh((x-y)/2)
sinh(x) - sinh(y) = 2 sinh((x-y)/2) cosh((x+y)/2)
cosh(x) + cosh(y) = 2 cosh((x+y)/2) cosh((x-y)/2)
cosh(x) - cosh(y) = 2 sinh((x+y)/2) sinh((x-y)/2)
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sinh(acosh(x)) = sqrt(x**2 - 1)
cosh(asinh(x)) = sqrt(x**2 + 1)
tanh(asech(x)) = sqrt(1 - x**2)
coth(acsch(x)) = sqrt(1 + x**2)
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