Question

The terminal side of angle o intersects the point (6,8). What is the exact value of csc(theta)

Answer 1

The figure for the intersection of side is,

For the angle theta perpendicular side is p=8 and base side is b=36.

Determine the length of hypotenuse side by using pythagoras theorem.

`\begin{gathered} h=\sqrt[]{p^2+b^2} \\ =\sqrt[]{(8)^2+(6)^2_{}} \\ =\sqrt[]{64+36} \\ =\sqrt[]{100} \\ =10 \end{gathered}`

Determine the trigonometric ratio csc theta for the given triangle.

`\begin{gathered} \csc \theta=(h)/(p) \\ =(10)/(8) \\ =(5)/(4) \end{gathered}`

So answer is 5/4.