Question

Trigonometry Functions of Any Angle CAA point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ.1) (12, 16) Find csc θ.

Answer 1

Answer:

A. 5/4

Explanation:

If the terminal side of angle θ is (12,16), then:

$x=12,y=16$

First, we find the value of the hypotenuse, r.

$\begin{gathered} r=\sqrt[]{x^2+y^2} \\ =\sqrt[]{12^2+16^2} \\ =\sqrt[]{400} \\ r=20\text{ units} \end{gathered}$

We know that cosecant is the inverse of sine.

Therefore:

$\begin{gathered} \cosec \theta=\frac{1}{\sin \theta}=\frac{Hypotenuse}{\text{Opposite}} \\ =\frac{20}{16} \\ =\frac{5}{4} \end{gathered}$

The correct choice is A.