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`

Step-by-step 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=√(a^2+b^2) \\ =√(8^2+6^2) \\ =√(64+36) \\ =√(100) \\ =10 \end{gathered}`

Now,

`\begin{gathered} csc\theta=(h)/(a) \\ =(10)/(8) \\ =(5)/(4) \end{gathered}`
`\begin{gathered} sec\theta=(h)/(b) \\ =(10)/(6) \\ =(5)/(3) \end{gathered}`

Final Answer:

Option(b) is correct.