Question

1 , 2 , 3 плиз, голова не варит уже 30 баллов​

Answer 1

$1)45^{0}=45^{0} *\frac{\pi }{180^{0} }=\frac{\pi }{4}\\\\150^{0}=150^{0}*\frac{\pi }{180^{0}}=\frac{5\pi }{6}\\\\\\2)Sin450^{0}=Sin(360^{0}+90^{0})=Sin90^{0}= 1\\\\Ctg110^{0}=Ctg(90^{0}+20^{0})=-tg20^{0}\\\\Sin450^{0}*Ctg110^{0}=1*(-tg20^{0})=-tg20^{0}\\\\\\3)Sin\alpha =\frac{1}{5}\\\\\frac{\pi }{2} <\alpha<\pi \ \Rightarrow Cos\alpha<0\\\\Cos\alpha=-\sqrt{1-Sin^{2}\alpha}=-\sqrt{1-(\frac{1}{5} )^{2}}=-\sqrt{1-\frac{1}{25}} =-\sqrt{\frac{24}{25}} =$

$=-\sqrt{\frac{4*6}{25} }=-\frac{2\sqrt{6} }{5}\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha }=-\frac{1}{5} *\frac{5}{2\sqrt{6}}=-\frac{1}{2\sqrt{6} }=-\frac{1*\sqrt{6} }{2\sqrt{6}*\sqrt{6} }=-\frac{\sqrt{6} }{12}$