If sin theta = -12/13 then what is csc theta?

The cosecant function \( \csc \theta \) is the reciprocal of the sine function \( \sin \theta \). This means:

\[
\csc \theta = \frac{1}{\sin \theta}
\]

Given that \( \sin \theta = -\frac{12}{13} \), we find \( \csc \theta \) as follows:

\[
\csc \theta = \frac{1}{-\frac{12}{13}} = -\frac{13}{12}
\]

Thus, \( \csc \theta = -\frac{13}{12} \).

Would you like more details on this or have any other questions?

Here are 5 related questions for further exploration:
1. What is \( \cos \theta \) if \( \sin \theta = -\frac{12}{13} \) and \( \theta \) is in the third quadrant?
2. How do you calculate the secant of an angle given its sine?
3. Can you find \( \tan \theta \) given \( \sin \theta = -\frac{12}{13} \)?
4. What is the value of \( \cot \theta \) for \( \sin \theta = -\frac{12}{13} \)?
5. How do you determine which quadrant \( \theta \) lies in based on the sign of \( \sin \theta \)?

**Tip:** Always check the quadrant of the angle to determine the correct sign of trigonometric functions.

Learn how to calculate the cosecant of an angle given that sin θ = -12/13. This problem involves using the reciprocal identity theorem, providing a clear step-by-step solution suitable for Grades 10-12 students.

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