Evaluate, if defined \( \sin \left(\sin ^{-1} \frac{1}{4}\right) \)

To evaluate \( \sin \left(\sin^{-1} \frac{1}{4}\right) \), we start by recognizing what \( \sin^{-1} \frac{1}{4} \) means. The expression \( \sin^{-1} \frac{1}{4} \) is the angle \( \theta \) such that \( \sin \theta = \frac{1}{4} \). Now, applying the sine function to this angle gives us: \[ \sin \left(\sin^{-1} \frac{1}{4}\right) = \frac{1}{4} \] Thus, the value of \( \sin \left(\sin^{-1} \frac{1}{4}\right) \) is \( \frac{1}{4} \).