The given function is
[tex]\sin A=\frac{5}{\sqrt[]{34}}[/tex]We know that secA is the inverse of cosA.
From the given function, we form the following triangle
Because the sine function is equivalent to the ratio between the opposite leg and the hypotenuse.
So, let's use the Pythagorean's theorem to find y
[tex]\begin{gathered} c^2=a^2+b^2 \\ (\sqrt[]{34})=y^2+5^2 \\ 34=y^2+25 \\ y^2=34-25 \\ y=\sqrt[]{9} \\ y=3 \end{gathered}[/tex]Once we have the adjacent leg, we can express the cosine function
[tex]\cos A=\frac{3}{\sqrt[]{34}}[/tex]Then, the inverse is
[tex]\sec A=\frac{\sqrt[]{34}}{3}[/tex]