2781.711004*(cos(10)+(0.0473/0.14974)*cos(2*10)-(1/4)*((0.0473/0.14974)^3)*cos(4*10))

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on Mar 17, 2025 at 2:34 am



You asked:

Evaluate the expression: 2781.711004(cos⁡(10)+0.04730.14974cos⁡(2⋅10)−14(0.04730.14974)3cos⁡(4⋅10))2781.711004 \left(\cos\left( 10 \right) + \frac{0.0473}{0.14974} \cos\left( 2 \cdot 10 \right) - \frac{1}{4} {\left( \frac{0.0473}{0.14974} \right)}^{3} \cos\left( 4 \cdot 10 \right)\right)

MathBot Answer:

2781.711004(cos⁡(10)+0.04730.14974cos⁡(2⋅10)−14(0.04730.14974)3cos⁡(4⋅10))=695427751cos⁡(10)250000−73592819058545567cos⁡(40)3357480402424000+328937326223cos⁡(20)374350000≈−1960.858522444922237707166388705085272781.711004 \left(\cos\left( 10 \right) + \frac{0.0473}{0.14974} \cos\left( 2 \cdot 10 \right) - \frac{1}{4} {\left( \frac{0.0473}{0.14974} \right)}^{3} \cos\left( 4 \cdot 10 \right)\right) = \frac{695427751 \cos{\left(10 \right)}}{250000} - \frac{73592819058545567 \cos{\left(40 \right)}}{3357480402424000} + \frac{328937326223 \cos{\left(20 \right)}}{374350000} \approx -1960.85852244492223770716638870508527

2781.711004(cos⁡(10)+0.04730.14974cos⁡(2⋅10)−14(0.04730.14974)3cos⁡(4⋅10))=(2781+7110041000000)⋅(cos⁡(10)+47310000⋅114974100000⋅cos⁡(2⋅10)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=(2781+177751250000)⋅(cos⁡(10)+47310000⋅114974100000⋅cos⁡(2⋅10)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+47310000⋅114974100000⋅cos⁡(2⋅10)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+47310000⋅1748750000⋅cos⁡(2⋅10)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+47310000⋅500007487⋅cos⁡(2⋅10)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+47310000⋅500007487⋅cos⁡(20)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅(47310000⋅114974100000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅(47310000⋅1748750000)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅(473⋅57487)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅(23657487)3⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅13227977125419685050303⋅cos⁡(4⋅10))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−14⋅13227977125419685050303⋅cos⁡(40))=695427751250000⋅(cos⁡(10)+23657487⋅cos⁡(20)−132279771251678740201212⋅cos⁡(40))=695427751250000⋅((23657487⋅cos⁡(20)+cos⁡(10))−132279771251678740201212⋅cos⁡(40))=695427751250000⋅(−132279771251678740201212⋅cos⁡(40)+23657487⋅cos⁡(20)+cos⁡(10))=−735928190585455673357480402424000⋅cos⁡(40)+695427751250000⋅cos⁡(10)+328937326223374350000⋅cos⁡(20)\begin{aligned}2781.711004 \left(\cos\left( 10 \right) + \frac{0.0473}{0.14974} \cos\left( 2 \cdot 10 \right) - \frac{1}{4} {\left( \frac{0.0473}{0.14974} \right)}^{3} \cos\left( 4 \cdot 10 \right)\right)&=\left(2781 + \frac{711004}{1000000}\right) \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}} \cdot \cos{\left(2 \cdot 10 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\left(2781 + \frac{177751}{250000}\right) \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}} \cdot \cos{\left(2 \cdot 10 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}} \cdot \cos{\left(2 \cdot 10 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{1}{\frac{7487}{50000}} \cdot \cos{\left(2 \cdot 10 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{50000}{7487} \cdot \cos{\left(2 \cdot 10 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{473}{10000} \cdot \frac{50000}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{14974}{100000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \left(\frac{473}{10000} \cdot \frac{1}{\frac{7487}{50000}}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \left(473 \cdot \frac{5}{7487}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \left(\frac{2365}{7487}\right)^{3} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \frac{13227977125}{419685050303} \cdot \cos{\left(4 \cdot 10 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{1}{4} \cdot \frac{13227977125}{419685050303} \cdot \cos{\left(40 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\cos{\left(10 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} - \frac{13227977125}{1678740201212} \cdot \cos{\left(40 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(\left(\frac{2365}{7487} \cdot \cos{\left(20 \right)} + \cos{\left(10 \right)}\right) - \frac{13227977125}{1678740201212} \cdot \cos{\left(40 \right)}\right)\\&=\frac{695427751}{250000} \cdot \left(- \frac{13227977125}{1678740201212} \cdot \cos{\left(40 \right)} + \frac{2365}{7487} \cdot \cos{\left(20 \right)} + \cos{\left(10 \right)}\right)\\&=- \frac{73592819058545567}{3357480402424000} \cdot \cos{\left(40 \right)} + \frac{695427751}{250000} \cdot \cos{\left(10 \right)} + \frac{328937326223}{374350000} \cdot \cos{\left(20 \right)}\end{aligned}

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