Math Problem Solver

\[-\left( \frac{3}{2} \right) \cdot \sin\left( \frac{49 \cdot \pi}{20} \right) + 1 = - \frac{3 \sqrt{2} \cdot \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)}{4} - \frac{3 \sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{4} + 1 \approx -0.48153251089270658928506037154016\]

\[\begin{aligned}-\left( \frac{3}{2} \right) \cdot \sin\left( \frac{49 \cdot \pi}{20} \right) + 1& = - \frac{3}{2} \cdot \sin{\left(49 \cdot \frac{\pi}{20} \right)} + 1\\& = - \frac{3}{2} \cdot \sin{\left(\frac{49}{20} \cdot \pi \right)} + 1\\& = - \frac{3}{2} \cdot \left(\frac{1}{2} \cdot \sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \frac{1}{2} \cdot \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)\right) + 1\\& = \left(- \frac{3}{4} \cdot \sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} - \frac{3}{4} \cdot \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)\right) + 1\\& = 1 - \frac{3}{4} \cdot \sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} - \frac{3}{4} \cdot \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)\end{aligned}\]