To determine which of the options is equivalent to \(\sin\left(\frac{2\pi}{15}\right)\), we will use the fact that \(\frac{2\pi}{15}\) is equivalent to \(12^\circ\) (since \(\frac{2\pi}{15} \times \frac{180}{\pi} = 12^\circ\)). Therefore, we have:
\[ \sin\left(\frac{2\pi}{15}\right) = \sin(12^\circ). \]
Now, let's evaluate the provided options:
- \(\sin(12^\circ)\): This is \( \sin\left(\frac{2\pi}{15}\right) \).
- \(\cos(24^\circ)\): This does not directly relate.
- \(\sin(24^\circ)\): This does not relate directly as \(24^\circ\) is not equal to \(\frac{2\pi}{15}\).
- \(\cos(12^\circ)\): This does not directly relate.
- \(\sin(12^\circ)\) is already confirmed to be equal to \(\sin\left(\frac{2\pi}{15}\right)\).
Since one direct equivalent to \(\sin\left(\frac{2\pi}{15}\right)\) is \(\sin(12^\circ)\), we can conclude:
The answer is \(\sin(12^\circ)\).