Question

!!!Urgent!!!
arcsin 8/17+arcsin 15/17=π/2

Answer 1

 

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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$\displaystyle\bf\\\textbf{Observam ca numerele 8, 15 si 17 formeaza un triplet pitagoric.}\\\\8^2+15^2=17^2\\64+225=289\\289=289~~~Corect\\\\\textbf{Vom rezolva problema in triunghiul dreptunghic.}\\(vezi~desenul~atasat)\\\\Rezolvare:\\\\sin~B=\frac{c.o.}{ip}=\frac{8}{17}\\\\sin~C=\frac{c.o.}{ip}=\frac{15}{17}\\\\\textbf{Functia arcsin este functia inversa a functiei sinus.}$

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$\displaystyle\bf\\\textbf{arcsin calculeaza masura unghiului al carui sinus se cunoaste.}\\\\Rezulta:\\\\arcsin \frac{8}{17}=m(\sphericalangle B)=\sphericalangle B\\\\arcsin \frac{15}{17}=m(\sphericalangle C)=\sphericalangle C\\\\In~\Delta ABC~din~desen~avem:\sphericalangle B+\sphericalangle C=90^o\\\\\implies~arcsin \frac{8}{17}+arcsin \frac{15}{17}=\sphericalangle B+\sphericalangle C=90^o=\pi/2\\\\\implies~\boxed{\bf~arcsin \frac{8}{17}+arcsin \frac{15}{17}=\frac{\pi}{2}}$