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

asked by guest
on Mar 17, 2025 at 2:34 am



You asked:

Evaluate the expression: 2781.711004(cos(10)+0.04730.14974cos(210)14(0.04730.14974)3cos(410))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(210)14(0.04730.14974)3cos(410))=695427751cos(10)25000073592819058545567cos(40)3357480402424000+328937326223cos(20)3743500001960.858522444922237707166388705085272781.711004 \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(210)14(0.04730.14974)3cos(410))=(2781+7110041000000)(cos(10)+47310000114974100000cos(210)14(47310000114974100000)3cos(410))=(2781+177751250000)(cos(10)+47310000114974100000cos(210)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+47310000114974100000cos(210)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+473100001748750000cos(210)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+47310000500007487cos(210)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+47310000500007487cos(20)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+23657487cos(20)14(47310000114974100000)3cos(410))=695427751250000(cos(10)+23657487cos(20)14(473100001748750000)3cos(410))=695427751250000(cos(10)+23657487cos(20)14(47357487)3cos(410))=695427751250000(cos(10)+23657487cos(20)14(23657487)3cos(410))=695427751250000(cos(10)+23657487cos(20)1413227977125419685050303cos(410))=695427751250000(cos(10)+23657487cos(20)1413227977125419685050303cos(40))=695427751250000(cos(10)+23657487cos(20)132279771251678740201212cos(40))=695427751250000((23657487cos(20)+cos(10))132279771251678740201212cos(40))=695427751250000(132279771251678740201212cos(40)+23657487cos(20)+cos(10))=735928190585455673357480402424000cos(40)+695427751250000cos(10)+328937326223374350000cos(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}