tan⁻¹(28.8/114.12)

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



You asked:

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

MathBot Answer:

\[\arctan\left( \frac{28.8}{114.12} \right) = \arctan{\left(\frac{80}{317} \right)} \approx 0.24720417874042396008688096943114\]

\[\begin{aligned}\arctan\left( \frac{28.8}{114.12} \right)& = \arctan{\left(\left(28 + \frac{8}{10}\right) \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\& = \arctan{\left(\left(28 + \frac{4}{5}\right) \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\& = \arctan{\left(\frac{144}{5} \cdot \frac{1}{114 + \frac{12}{100}} \right)}\\& = \arctan{\left(\frac{144}{5} \cdot \frac{1}{114 + \frac{3}{25}} \right)}\\& = \arctan{\left(\frac{144}{5} \cdot \frac{1}{\frac{2853}{25}} \right)}\\& = \arctan{\left(\frac{80}{317} \right)}\end{aligned}\]

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