a) Wiedząc, że kąt α jest ostry i sin α=√2/5 oblicz cos α i tg α b) Wiedząc, że kąt α jest ostry i cos α=√3/4, oblicz sin α i tg α Z góry dziękuje za pomoc (:

a) [latex]sin alpha = frac{ sqrt{2} }{5} \ \ sin^{2} alpha +cos^{2} alpha =1\ \ cos alpha = sqrt{1-sin^{2} alpha } \ \ cos= sqrt{1-( frac{ sqrt{2} }{5})^{2} } = sqrt{1- frac{2}{25} } = sqrt{ frac{23}{25} } = frac{ sqrt{23} }{5} \ \ tg alpha = frac{sin alpha }{cos alpha } \ \ tg alpha = frac{ frac{ sqrt{2} }{5} }{ frac{ sqrt{23} }{5} } = frac{ sqrt{2} }{5}* frac{5}{ sqrt{23} } = frac{ sqrt{2} }{ sqrt{23} } = frac{ sqrt{46} }{23} [/latex] b) [latex]cos alpha = frac{ sqrt{3} }{4} \ \ sin^{2} alpha +cos^{2} alpha =1 \ \ sin alpha = sqrt{1-cos^{2} alpha } \ \ sin alpha = sqrt{1-( frac{ sqrt{3} }{4})^{2} } = sqrt{1- frac{3}{16} } = sqrt{ frac{13}{16} } = frac{ sqrt{13} }{4} \ \ tg alpha = frac{sin alpha }{cos alpha } \ \ tg alpha = frac{ frac{ sqrt{13} }{4} }{ frac{ sqrt{3} }{4} } =frac{ sqrt{13} }{4}* frac{4}{ sqrt{3} } = frac{ sqrt{13} }{ sqrt{3} } = frac{ sqrt{39} }{3} [/latex]