Step-by-step explanation and Answers:
[tex](\frac{1}{\sqrt{10}},\frac{3}{\sqrt{10}})[/tex] is in the format (cos, sin). So, adjacent = 1, opposite = 3, hypotenuse = [tex]\sqrt{10}[/tex]
sin = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{10}}(\frac{\sqrt{10}}{\sqrt{10}})[/tex] = [tex]\frac{3\sqrt{10}}{10}[/tex]
cos = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{1}{\sqrt{10}}(\frac{\sqrt{10}}{\sqrt{10}})[/tex] = [tex]\frac{\sqrt{10}}{10}[/tex]
tan = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{1}[/tex] = 3
csc = [tex]\frac{hypotenuse}{opposite}[/tex] = [tex]\frac{\sqrt{10}}{3}[/tex]
sec = [tex]\frac{hypotenuse}{adjacent}[/tex] = [tex]\frac{\sqrt{10}}{1}[/tex] = [tex]\sqrt{10}[/tex]
cot = [tex]\frac{adjacent}{opposite}[/tex] = [tex]\frac{1}{3}[/tex]
