step 1
Find the hypotenuse of the right triangle
applying Pythagorean theorem
c^2=2^2+3^2
c^2=4+9
[tex]c=\sqrt[]{13}[/tex]
step 2
Find sin(theta)
we have
[tex]\sin (\theta)=\frac{2}{\sqrt[]{13}}[/tex]
simplify
[tex]\sin (\theta)=\frac{2}{\sqrt[]{13}}=\frac{2\sqrt[\square]{13}}{13}[/tex]
opposite side divided by the hypotenuse
step 3
Find cos(theta)
[tex]\cos (\theta)=\frac{3}{\sqrt[\square]{13}}[/tex]
adjacent side divided by the hypotenuse
simplify
[tex]\cos (\theta)=\frac{3}{\sqrt[\square]{13}}=\frac{3\sqrt[]{13}}{13}[/tex]
step 4
find tan(theta)
[tex]\tan (\theta)=\frac{2}{3}[/tex]
opposite side divided by the adjacent side
step 5
find cot(theta)
[tex]\cot (\theta)=\frac{1}{\tan (\theta)}=\frac{3}{2}[/tex]
adjacent side divided by the opposite side
step 6
Find sec(theta)
[tex]\sec (\theta)=\frac{1}{\cos (\theta)}=\frac{\sqrt[]{13}}{3}[/tex]
hypotenuse divided by the adjacent side
step 7
Find csc(theta)
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}=\frac{\sqrt[]{13}}{2}[/tex]
hypotenuse divided by the opposite side
