\alpha &= \measuredangle BAE \\
x_1 &= a \sin \alpha \\
y &= a \cos \alpha \\
y_1 &= a \sin \left( \frac{\pi}{6} - \alpha \right) \\
&= a \left( \frac{1}{2} \cos \alpha - \frac{\sqrt{3}}{2} \sin \alpha \right) \\
x &= a \cos \left( \frac{\pi}{6} - \alpha \right) \\
&= a \left( \frac{\sqrt{3}}{2} \cos \alpha + \frac{1}{2} \sin \alpha \right) \\