# Solving an example with imaginary units. \theta=\arctan(\sqrt{3}+2) \theta=75^\circ=5\pi/12

Umaiza Hutton 2022-02-25 Answered
Solving an example with imaginary units.
$\theta =\mathrm{arctan}\left(\sqrt{3}+2\right)$
$\theta ={75}^{\circ }=5\frac{\pi }{12}$
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## Expert Answer

Ollie Castillo
Answered 2022-02-26 Author has 5 answers
We will use the half-angle formula for tangent:
$\mathrm{tan}\frac{\theta }{2}=\frac{1-\mathrm{cos}\left(\theta \right)}{\mathrm{sin}\left(\theta \right)}$
We want to get $2+\sqrt{3}$. Remembering the basic values of sine and cosine, I see that
$2+\sqrt{3}=\frac{1+\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\mathrm{cos}\frac{5\pi }{6}}{\mathrm{sin}\frac{5\pi }{6}}=\mathrm{tan}\frac{5\pi }{12}$
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