Answer:
A. 5/4
Explanation:
If the terminal side of angle θ is (12,16), then:
[tex]x=12,y=16[/tex]
First, we find the value of the hypotenuse, r.
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ =\sqrt[]{12^2+16^2} \\ =\sqrt[]{400} \\ r=20\text{ units} \end{gathered}[/tex]
We know that cosecant is the inverse of sine.
Therefore:
[tex]\begin{gathered} \cosec \theta=\frac{1}{\sin \theta}=\frac{Hypotenuse}{\text{Opposite}} \\ =\frac{20}{16} \\ =\frac{5}{4} \end{gathered}[/tex]
The correct choice is A.
