-(3/2) * sin(49 pi /20) + 1

asked by guest
on Nov 26, 2024 at 2:35 pm



You asked:

Evaluate the expression: −(32)⋅sin⁡(49π20)+1-\left( \frac{3}{2} \right) \cdot \sin\left( \frac{49 \pi}{20} \right) + 1

MathBot Answer:

−(32)⋅sin⁡(49π20)+1=−32⋅(14+54)4−3258−584+1≈−0.48153251089270658928506037154016-\left( \frac{3}{2} \right) \cdot \sin\left( \frac{49 \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

−(32)⋅sin⁡(49π20)+1=−32⋅sin⁡(49⋅π20)+1=−32⋅sin⁡(4920⋅π)+1=−32⋅(12⋅2⋅58−18⋅5+12⋅2⋅(14+14⋅5))+1=(−34⋅2⋅58−18⋅5−34⋅2⋅(14+14⋅5))+1=1−34⋅2⋅58−18⋅5−34⋅2⋅(14+14⋅5)\begin{aligned}-\left( \frac{3}{2} \right) \cdot \sin\left( \frac{49 \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}

+ Submit Question