arctan((7sqrt(3)/2)/3.5)

asked by guest
on Oct 23, 2024 at 9:18 am



You asked:

Evaluate the expression: \(\arctan\left( \frac{\frac{7 \cdot \sqrt{3}}{2}}{3.5} \right)\)

MathBot Answer:

\[\arctan\left( \frac{\frac{7 \cdot \sqrt{3}}{2}}{3.5} \right) = \frac{\pi}{3} \approx 1.04719755119659774615421446109317\]

\[\begin{aligned}\arctan\left( \frac{\frac{7 \cdot \sqrt{3}}{2}}{3.5} \right)& = \arctan{\left(7 \cdot \sqrt{3} \cdot \frac{1}{2} \cdot \frac{1}{3 + \frac{5}{10}} \right)}\\& = \arctan{\left(7 \cdot \sqrt{3} \cdot \frac{1}{2} \cdot \frac{1}{3 + \frac{1}{2}} \right)}\\& = \arctan{\left(7 \cdot \sqrt{3} \cdot \frac{1}{2} \cdot \frac{1}{\frac{7}{2}} \right)}\\& = \arctan{\left(7 \cdot \sqrt{3} \cdot \frac{1}{7} \right)}\\& = \arctan{\left(\sqrt{3} \right)}\\& = \frac{\pi}{3}\end{aligned}\]

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