Question

arcsin 3/5 + arcsin 4/5 = pi/2 va rogggg

Answer 1

$\displaystyle\bf\\Sa~se~arate~ca~arcsin\bigg(\frac{3}{5}\bigg)+arcsin\bigg(\frac{4}{5}\bigg)=\frac{\pi}{2}\\\\Rezolvare:~~(Vezi~desenul~atasat.)\\\\Desenam~\Delta ABC~dreptunghic~cu~catetele~AB=4~cm~si~AC=3~cm\\\\Ipotenuza~BC~o~calculam~cu~Pitagora.\\\\BC=\sqrt{AB^2+AC^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5 cm.$  

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.$\displaystyle\bf\\Unghiurile~ascutite~ale~triunghiului~dreptunghic~sunt~complementare.\\\\\implies~m(\angle B)+m(\angle C)=90^o\\\\sin B = \frac{c.o.}{i}=\frac{AC}{BC}=\frac{3}{5}\\\\sin C = \frac{c.o.}{i}=\frac{AB}{BC}=\frac{4}{5}$

.$\displaystyle\bf\\Daca~stim~stim~sinusul~unui~unghi,~putem~calcula~masura~unghiului\\folosind~functia~inversa~(arcsin)\\\\arcsin\bigg(\frac{3}{5}\Big)=m(\angle B)\\\\arcsin\bigg(\frac{4}{5}\Big)=m(\angle C)\\\\arcsin\bigg(\frac{3}{5}\Big)+arcsin\bigg(\frac{4}{5}\Big)=m(\angle B)+m(\angle C)=90^o=\frac{\pi}{2}$