Question

знаючи,що sin a = 2/5 ,обчисліть cos a,tg a ,ctg a за умови,що: 0<а<п/2

Answer 1

$\displaystyle\bf\\0<\alpha <\frac{\pi }{2} \ \ \Rightarrow \ Cos\alpha >0 \ , \ tg\alpha >0 \ , \ Ctg\alpha >0\\\\\\Cos\alpha =\sqrt{1-Sin^{2} \alpha } =\sqrt{1-\Big(\frac{2}{5} \Big)^{2} } =\sqrt{1-\frac{4}{25} } =\sqrt{\frac{21}{25} } =\frac{\sqrt{21} }{5} \\\\\\tg\alpha =\frac{Sin\alpha }{Cos\alpha } =\frac{2}{5} :\frac{\sqrt{21} }{5} =\frac{2}{5} \cdot\frac{5}{\sqrt{21} }=\frac{2}{\sqrt{21} }\\\\\\Ctg\alpha =\frac{1}{tg\alpha } =1:\frac{2}{\sqrt{21} } =\frac{\sqrt{21} }{2}$