Given:
The points is (6,8)
Required:
To find
[tex]csc\theta\text{ and sec}\theta[/tex]Explanation:
Let a represent length of the opposite side:
[tex]a=8[/tex]Let b represent the length of the adjacent side:
[tex]b=6[/tex]The length of the hypotenuse is:
[tex]\begin{gathered} h=\sqrt{a^2+b^2} \\ =\sqrt{8^2+6^2} \\ =\sqrt{64+36} \\ =\sqrt{100} \\ =10 \end{gathered}[/tex]Now,
[tex]\begin{gathered} csc\theta=\frac{h}{a} \\ =\frac{10}{8} \\ =\frac{5}{4} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{h}{b} \\ =\frac{10}{6} \\ =\frac{5}{3} \end{gathered}[/tex]Final Answer:
Option(b) is correct.