[latex]a)\ sina= frac{1}{4} \ cos^2a =1-sin^2a=1-(frac{1}{4})^2=1-frac{1}{16}=frac{15}{16}\ cosa=sqrt{frac{15}{16} }=frac{1}{4}*sqrt{15}\ tga= frac{sina}{cosa}=frac{frac{1}{4}}{frac{1}{4}*sqrt{15}} =frac{1}{4}* frac{4}{sqrt{15}}= frac{1}{sqrt{15} }= frac{sqrt{15}}{15} \ ctga= frac{1}{tga}=sqrt{15}\ b)\ [/latex] [latex]cosa= frac{sqrt3}{4} \ sin^2=1-cos^a=1-( frac{sqrt3}{4} )^2=1- frac{3}{16}= frac{13}{16}\ sina=sqrt{ frac{13}{16}}= frac{1}{4}*sqrt{13}\ tga= frac{sina}{cosa}=frac{frac{sqrt{13} }{4}}{frac{sqrt3}{4}} =frac{sqrt{13} }{4}* frac{4}{ sqrt{3}} = frac{sqrt{13} }{sqrt3}\ ctga= frac{1}{tga}=frac{sqrt{3}}{sqrt{13}} \ [/latex] [latex]c)\ tga=3\ ctga= frac{1}{tg}= frac{1}{3} \ tg= frac{a}{b} =3\ sina= frac{a}{c}\ c^2=a^2+b^2=3^2+1^2=9+1=10\ c=sqrt{10}\ sina= frac{3}{sqrt{10}}* frac{sqrt{10}}{sqrt{10}}=0,3sqrt{10}\ cosa= frac{sina}{tga}= frac{0,3sqrt{10}}{3} =0,1sqrt{10}[/latex]
