tan⁻¹(28.8/114.12)

asked by guest
on Jan 14, 2025 at 7:08 am



You asked:

Evaluate the expression: arctan⁡(28.8114.12)\arctan\left( \frac{28.8}{114.12} \right)

MathBot Answer:

arctan⁡(28.8114.12)=arctan⁡(80317)≈0.24720417874042396008688096943114\arctan\left( \frac{28.8}{114.12} \right) = \arctan{\left(\frac{80}{317} \right)} \approx 0.24720417874042396008688096943114

arctan⁡(28.8114.12)=arctan⁡((28+810)⋅1114+12100)=arctan⁡((28+45)⋅1114+12100)=arctan⁡(1445⋅1114+12100)=arctan⁡(1445⋅1114+325)=arctan⁡(1445⋅1285325)=arctan⁡(80317)\begin{aligned}\arctan\left( \frac{28.8}{114.12} \right)&=\arctan{\left(\left(28 + \frac{8}{10}\right) \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\&=\arctan{\left(\left(28 + \frac{4}{5}\right) \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\&=\arctan{\left(\frac{144}{5} \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\&=\arctan{\left(\frac{144}{5} \cdot \frac{1}{114 + \frac{3}{25}} \right)}\\&=\arctan{\left(\frac{144}{5} \cdot \frac{1}{\frac{2853}{25}} \right)}\\&=\arctan{\left(\frac{80}{317} \right)}\end{aligned}

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