To determine which of the given options is not a value of \( \theta \) when \( \sin \theta = -1 \), we first need to understand the conditions under which \( \sin \theta = -1 \).
The sine function equals -1 at:
\[ \theta = \frac{3\pi}{2} + 2k\pi \]
where \( k \) is any integer (because the sine function has a period of \( 2\pi \)).
Now let's evaluate each of the provided options:
- \( \frac{3\pi}{2} \) – This is a value where \( \sin \theta = -1 \).
- \( \pi \) – This does not equal -1 for the sine function.
- \( -\frac{\pi}{2} \) – This does not equal -1 for the sine function.
- \( \frac{7\pi}{2} \) – This can be simplified as \( \frac{7\pi}{2} = \frac{3\pi}{2} + 2\pi \), so it does equal -1 for the sine function.
- \( \pi \) again, as stated before, does not equal -1.
From this analysis, the options that do not yield \( \sin \theta = -1 \) are:
- \( \pi \)
- \( -\frac{\pi}{2} \)
Thus, out of the choices provided, \( \pi \) is one of the definite answers.
Therefore, the option that is not a value of \( \theta \) when \( \sin \theta = -1 \) is:
\[ \pi \]