Marinada '22

[lang=hr] Doktorica Lili Štriga jako voli maškare pa je u Našoj maloj klinici organizirala kostimiranu potragu za blagom. Ipak, svaki je natjecatelj igrom slučaja zapeo na nekom trigonometrijskom zadatku koji ga navodi na idući trag. Jesu li zadaci zaista preteški?\\ \\ Doktor Veljko Kunić muči se sa sljedećim:\\ Neka je $\Delta ABC$ šiljastokutni trokut s kutevima $\alpha$, $\beta$ i $\gamma$. Uzlaznim redoslijedom navedi kvadrante u kojima može ležati točka $(\cos \beta - \sin \alpha, \, \sin \beta - \cos \alpha)$. Primjerice, ako može biti u sva četiri kvadranta, upiši $1234$. [/lang] [lang=en] Doctor Lili Štriga loves Halloween so she organized a special Halloween scavenger hunt in Our Little Clinic. Coincidentally, every contestant was stuck trying to solve a clue based on trigonometry. Are these exercises really too hard?\\ \\ Doctor Veljko Kunić is having trouble solving this:\\ Let $\Delta ABC$ be a triangle with three acute angles: $\alpha$, $\beta$ and $\gamma$. List the possible quadrants in which point $(\cos \beta - \sin \alpha, \, \sin \beta - \cos \alpha)$ can be located in ascending order. For example, if it can lie in all four quadrants, write $1234$. [/lang]