Consider ca enuntul suna asa:
"Sa se arate ca arcsin 8/17 + arcsin 15/17 = π / 2
In loc de π / 2 voi scrie 90°.
Vezi desenul atasat.
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[tex]\displaystyle\bf\\\textbf{Observam ca numerele 8, 15 si 17 formeaza un triplet pitagoric.}\\\\8^2+15^2=17^2\\64+225=289\\289=289~~~Corect\\\\\textbf{Vom rezolva problema in triunghiul dreptunghic.}\\(vezi~desenul~atasat)\\\\Rezolvare:\\\\sin~B=\frac{c.o.}{ip}=\frac{8}{17}\\\\sin~C=\frac{c.o.}{ip}=\frac{15}{17}\\\\\textbf{Functia arcsin este functia inversa a functiei sinus.}[/tex]
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[tex]\displaystyle\bf\\\textbf{arcsin calculeaza masura unghiului al carui sinus se cunoaste.}\\\\Rezulta:\\\\arcsin \frac{8}{17}=m(\sphericalangle B)=\sphericalangle B\\\\arcsin \frac{15}{17}=m(\sphericalangle C)=\sphericalangle C\\\\In~\Delta ABC~din~desen~avem:\sphericalangle B+\sphericalangle C=90^o\\\\\implies~arcsin \frac{8}{17}+arcsin \frac{15}{17}=\sphericalangle B+\sphericalangle C=90^o=\pi/2\\\\\implies~\boxed{\bf~arcsin \frac{8}{17}+arcsin \frac{15}{17}=\frac{\pi}{2}}[/tex]
