Question

For a standard-position angle determined by the point (x, y), what are the values of the trigonometric functions?For the point (6, 8), find csc θ and sec θ.

Answer 1

Given:

The points is (6,8)

Required:

To find

$csc\theta\text{ and sec}\theta$

Explanation:

Let a represent length of the opposite side:

$a=8$

Let b represent the length of the adjacent side:

$b=6$

The length of the hypotenuse is:

$\begin{gathered} h=\sqrt{a^2+b^2} \\ =\sqrt{8^2+6^2} \\ =\sqrt{64+36} \\ =\sqrt{100} \\ =10 \end{gathered}$

Now,

$\begin{gathered} csc\theta=\frac{h}{a} \\ =\frac{10}{8} \\ =\frac{5}{4} \end{gathered}$$\begin{gathered} sec\theta=\frac{h}{b} \\ =\frac{10}{6} \\ =\frac{5}{3} \end{gathered}$

Final Answer:

Option(b) is correct.