Select your answer \( \begin{array}{l}\text { What is } \sin \left(\frac{\pi}{12}\right) ? \\ -0.34 \\ 0.26 \\ 0.48 \\ 0.65\end{array} \)

To find \(\sin\left(\frac{\pi}{12}\right)\), we can use the sine angle subtraction formula. Notably, \(\frac{\pi}{12}\) can be expressed as \(\frac{\pi}{3} - \frac{\pi}{4}\). Using the formula: \[ \sin(a - b) = \sin a \cos b - \cos a \sin b \] where \(a = \frac{\pi}{3}\) and \(b = \frac{\pi}{4}\), we have: \[ \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}, \quad \cos\left(\frac{\pi}{3}\right) = \frac{1}{2}, \quad \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}, \quad \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \] Substituting these values in, we calculate: \[ \sin\left(\frac{\pi}{12}\right) = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{1}{2} \cdot \frac{\sqrt{2}}{2} = \frac{\sqrt{6} - \sqrt{2}}{4} \] Calculating \(\frac{\sqrt{6} - \sqrt{2}}{4}\) gives us approximately 0.2588, which rounds to 0.26. Therefore, the correct answer is: 0.26