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Inverse tangent function

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Algebra and Trigonometry

Definition

The inverse tangent function, denoted as $\text{tan}^{-1}(x)$ or $\arctan(x)$, returns the angle whose tangent is $x$. It is the inverse operation of the tangent function and has a range of $-\frac{\pi}{2}$ to $\frac{\pi}{2}$.

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5 Must Know Facts For Your Next Test

  1. The inverse tangent function is defined for all real numbers.
  2. $\arctan(1) = \frac{\pi}{4}$ because $\tan(\frac{\pi}{4}) = 1$.
  3. The graph of $y = \arctan(x)$ is an odd function, symmetric about the origin.
  4. $y = \arctan(x)$ has horizontal asymptotes at $y = \pm \frac{\pi}{2}$.
  5. In solving trigonometric equations, the principal value of $\arctan(x)$ lies within the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

Review Questions

  • What is the range of the inverse tangent function?
  • Calculate $\arctan(0)$. What angle does this correspond to?
  • Explain why $y = \arctan(x)$ has horizontal asymptotes at $ y= \pm \frac{\pi}{2}$.
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