To solve the problem, we need to understand the relationship between the cosecant function and the unit circle. Let's break it down step-by-step:
1. Unit Circle Definition: On the unit circle, a point [tex]\(P(x, y)\)[/tex] is defined for an angle [tex]\(\theta\)[/tex], where:
- [tex]\(x = \cos \theta\)[/tex]
- [tex]\(y = \sin \theta\)[/tex]
2. Cosecant Function: The cosecant function, [tex]\(\csc \theta\)[/tex], is the reciprocal of the sine function:
- [tex]\(\csc \theta = \frac{1}{\sin \theta}\)[/tex]
3. Substitute Sin [tex]\(\theta\)[/tex]:
- Since [tex]\(y = \sin \theta\)[/tex], we can substitute [tex]\(y\)[/tex] into the cosecant function formula.
- Therefore, [tex]\(\csc \theta = \frac{1}{\sin \theta} = \frac{1}{y}\)[/tex]
Thus, the value of [tex]\(\csc \theta\)[/tex] is [tex]\(\frac{1}{y}\)[/tex].
Consequently, the correct choice is:
[tex]\[ \boxed{3} \][/tex]
