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[tex]cos(a+b+c)=cos(a)cos(b)cos(c)-sin(a)sin(b)cos(c)-sin(a)cos(b)sin(c)+cos(a)sin(b)sin(c)[/tex]
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Cosinus
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Vektormannen
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Dette er vel rett fram? Benytter identitetene [tex]\cos(u + v) = \cos u \cos v - \sin u sin v[/tex] og [tex]\sin(u + v) = \sin u \cos v + \cos u \sin v[/tex].
[tex]\cos(a + b + c) = \cos((a + b) + c) = \cos((a + b) + c) = \cos(a + b) \cos(c) - \sin(a+b) \sin(c)[/tex]
[tex]\cos(a+b) = \cos a \cos b - \sin a \sin b[/tex]
[tex]\sin(a+b) = \sin a \cos b + \cos a \sin b[/tex]
Setter inn:
[tex]\cos(a + b + c) \\ = \cos((a + b) + c) = \cos(a + b) \cos(c) - \sin(a+b) \sin(c)\\ = \left(\cos a \cos b - \sin a \sin b\right) \cos c - \left(\sin a \cos b + \cos a \sin b\right) \sin c \\ = \cos a \cos b \cos c - \sin a \sin b \cos c - \sin a \cos b \sin c - \cos a \sin b \sin c[/tex]
Edit: retta noe småpirk.
[tex]\cos(a + b + c) = \cos((a + b) + c) = \cos((a + b) + c) = \cos(a + b) \cos(c) - \sin(a+b) \sin(c)[/tex]
[tex]\cos(a+b) = \cos a \cos b - \sin a \sin b[/tex]
[tex]\sin(a+b) = \sin a \cos b + \cos a \sin b[/tex]
Setter inn:
[tex]\cos(a + b + c) \\ = \cos((a + b) + c) = \cos(a + b) \cos(c) - \sin(a+b) \sin(c)\\ = \left(\cos a \cos b - \sin a \sin b\right) \cos c - \left(\sin a \cos b + \cos a \sin b\right) \sin c \\ = \cos a \cos b \cos c - \sin a \sin b \cos c - \sin a \cos b \sin c - \cos a \sin b \sin c[/tex]
Edit: retta noe småpirk.
Last edited by Vektormannen on 02/10-2008 09:45, edited 1 time in total.
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