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

asked by guest
on Nov 26, 2024 at 2:33 pm



You asked:

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

MathBot Answer:

−32sin⁡(49π20)+1=1−3258−58+2⋅(14+54)≈−0.51869768868200439704261597448187\frac{-3}{2 \sin\left( \frac{49 \pi}{20} \right)} + 1 = 1 - \frac{3}{\sqrt{2} \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{\sqrt{5}}{4}\right)} \approx -0.51869768868200439704261597448187

−32sin⁡(49π20)+1=−3⋅12⋅sin⁡(49⋅π20)+1=−3⋅12⋅sin⁡(4920⋅π)+1=−3⋅12⋅(12⋅2⋅58−18⋅5+12⋅2⋅(14+14⋅5))+1=−3⋅12⋅58−18⋅5+2⋅(14+14⋅5)+1=1−3⋅12⋅58−18⋅5+2⋅(14+14⋅5)\begin{aligned}\frac{-3}{2 \sin\left( \frac{49 \pi}{20} \right)} + 1&=-3 \cdot \frac{1}{2 \cdot \sin{\left(49 \cdot \frac{\pi}{20} \right)}} + 1\\&=-3 \cdot \frac{1}{2 \cdot \sin{\left(\frac{49}{20} \cdot \pi \right)}} + 1\\&=-3 \cdot \frac{1}{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\\&=-3 \cdot \frac{1}{\sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)} + 1\\&=1 - 3 \cdot \frac{1}{\sqrt{2} \cdot \sqrt{\frac{5}{8} - \frac{1}{8} \cdot \sqrt{5}} + \sqrt{2} \cdot \left(\frac{1}{4} + \frac{1}{4} \cdot \sqrt{5}\right)}\end{aligned}

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