5-kosougli sferni trougao
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5-Kosougli sferni trougaoTRANSCRIPT
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 1oktobar 2011. godine
KOSOUGLI SFERNI TROUGAO
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 2oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 3oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 4oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 5oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 6oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 7oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 8oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 9oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 10oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 11oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 12oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 13oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 14oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 15oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 16oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 17oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 18oktobar 2011. godine
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 19
REZIME
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 20
KOSINUSNA TEOREMA
Kosinus strane jednak je zbiru proizvoda kosinusa naspramnih strana, proizvodu sinusa istih tih strana i kosinusa naspramnog ugla.
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cos cos cos sin sin cos
cos cos cos sin sin cos
cos cos cos sin sin cos
a b c b c
b a c a c
c a b a b
• Ako su a, b, c strane a α, β i γ uglovi sfernog trougla ABC onda vrijedi:
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 21
cos cos cos sin sin cos
cos cos cos sin sin cos
cos cos cos sin sin cos
a
b
c
• Kosinus ugla jednak je zbiru negativnog proizvoda kosinusa naspramnih uglova, proizvodu sinusa ista ta dva ugla i kosinusa naspramne strane.
cos cos coscos
sin sin
a b c
a b
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Priredio: mr.sc. Edin Hadžimustafić, viši asistent 22
SINUSNA TEOREMA Ako su a, b, c strane a α, β i γ uglovi
sfernog trougla ABC onda vrijedi:
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sin sin sin
sin sin sina b c
• Pomoću sinusne teoreme može se riješiti onaj sferni trougao kod koga su poznate dvije strane i ugao naspram jedne od njih i onaj sferni trougao kod koga su poznata dva ugla i stranica naspram jednog od njih.