Prosze o szybko pomoc !!! praca potrzebna gotowa na jutro ,na egzamin semestralny ;-( Praca w zalaczniju

1. a) Z własności trójkąta prostokątnego o katach ostrych 30⁰ i 60⁰ : |AC| = a√3 = 4√3 |BC| = 2a = 2 × 4 = 8 b) Z własności kąta prostokątnego równoramiennego (o katach ostrych 45⁰ : |AC| = √2 |AB| = a√2 = √2 × √2 = 2 [latex]2.\\sinalpha = frac{12}{13}\\cos^{2}alpha = 1 - sin^{2}alpha = 1 - (frac{12}{13})^{2} = frac{169}{169}-frac{144}{169} = frac{25}{169}\cosalpha = sqrtfrac{25}{169} = frac{5}{13}\\tgalpha = frac{sinalpha}{cosalpha} = frac{12}{13}:frac{5}{13} = frac{12}{13}*frac{12}{5} = frac{12}{5}\\ctgalpha = frac{1}{tgalpha} = frac{5}{12} [/latex] [latex]3.\\sinalpha = frac{2}{3}\\cos^{2}alpha = 1 - sin^{2}alpha = 1 - (frac{2}{3})^{2} = frac{9}{9}-frac{4}{9}} = frac{5}{9}}[/latex] [latex]1 - 3cos^{2}alpha = 1 - 3*frac{5}{9} = 1-frac{5}{3} = frac{3}{3}-frac{5}{3} = -frac{2}{3}[/latex] [latex]4.\\L = frac{sinalpha+cosalpha}{cosalpha} = frac{cosalpha}{cosalpha} + frac{sinalpha}{cosalpha} = 1 + tgalpha\\P = 1+tgalpha\\L = P[/latex] [latex]5.\\frac{sin150^{o}+cos120^{o}}{6*tg120^{o}} = frac{sin(180^{o}-30^{o})+cos(180^{o}-30^{o})}{6*tg(180^{o}-60^{o})} =frac{sin30^{o}-cos60^{o}}{6*(-tg60^{o})}=\\=frac{frac{1}{2}-frac{1}{2}}{6*(-sqrt{3})} = 0[/latex]