Mathc initiation/Fichiers h : c77a5

Sommaire

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Liste des équations trigonométriques étudiées

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sin(x)**2 + cos(x)**2 = 1

sec(x)**2 - tan(x)**2 = 1
csc(x)**2 - cot(x)**2 = 1

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cos(x+y) = cos(x) cos(y) - sin(x) sin(y)
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)


tan(x+y) = (tan(y)+tan(x)) / (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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