Pregunta
Evaluate the following: \( \boldsymbol{\operatorname { t a n }}^{-1}(\sqrt{3} / 3) \)
Ask by Clarke Lane. in Puerto Rico
Dec 03,2024
Solución de inteligencia artificial de Upstudy
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The value is approximately 0.524 or \( \frac{\pi}{6} \) radians.
Solución
Calculate or simplify the expression \( \arctan(\sqrt(3)/3) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arctan\left(\frac{\sqrt{3}}{3}\right)\)
- step1: Calculate the trigonometric value:
\(\frac{\pi }{6}\)
The value of \( \arctan\left(\frac{\sqrt{3}}{3}\right) \) is approximately 0.524 or \( \frac{\pi}{6} \) in radians.
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Simplifique esta solución Bonus Knowledge
The expression \( \tan^{-1}(\sqrt{3}/3) \) represents the angle whose tangent is \( \sqrt{3}/3 \). Recall that the tangent of \( 30^\circ \) (or \( \pi/6 \) in radians) is \( \sqrt{3}/3 \). Therefore, \[ \tan^{-1}(\sqrt{3}/3) = 30^\circ \] or in radians: \[ \tan^{-1}(\sqrt{3}/3) = \frac{\pi}{6}. \]
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