Skip to main content
Indietro

Inverse Trigonometric Functions - Precalculus

I pulsanti di controllo sono stati cambiati in modalità "navigazione".
1/20

Termini in questo insieme (20)

  • What is the inverse sine function?
    The inverse sine function, denoted by \(\sin^{-1}\), is the inverse of the restricted sine function \(y=\sin x\) with domain \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\).
  • What is the domain and range of the inverse sine function?
    Domain: \([-1,1]\), Range: \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
  • What is the inverse cosine function?
    The inverse cosine function, denoted by \(\cos^{-1}\), is the inverse of the restricted cosine function \(y=\cos x\) with domain \(0 \leq x \leq \pi\).
  • What is the domain and range of the inverse cosine function?
    Domain: \([-1,1]\), Range: \([0, \pi]\).
  • What is the inverse tangent function?
    The inverse tangent function, denoted by \(\tan^{-1}\), is the inverse of the restricted tangent function \(y=\tan x\) with domain \(-\frac{\pi}{2} < x < \frac{\pi}{2}\).
  • What is the domain and range of the inverse tangent function?
    Domain: \(\mathbb{R}\) (all real numbers), Range: \((-\frac{\pi}{2}, \frac{\pi}{2})\).
  • What is the property of the sine function and its inverse?
    \(\sin(\sin^{-1} x) = x\) for every \(x \in [-1,1]\).
  • What is the property of the inverse sine function and sine?
    \(\sin^{-1}(\sin x) = x\) for every \(x \in [-\frac{\pi}{2}, \frac{\pi}{2}]\).
  • What is the property of the cosine function and its inverse?
    \(\cos(\cos^{-1} x) = x\) for every \(x \in [-1,1]\).
  • What is the property of the inverse cosine function and cosine?
    \(\cos^{-1}(\cos x) = x\) for every \(x \in [0, \pi]\).
  • What is the property of the tangent function and its inverse?
    \(\tan(\tan^{-1} x) = x\) for every real number \(x\).
  • What is the property of the inverse tangent function and tangent?
    \(\tan^{-1}(\tan x) = x\) for every \(x \in (-\frac{\pi}{2}, \frac{\pi}{2})\).
  • How to evaluate \(\cot\left(\sin^{-1}\left(-\frac{1}{3}\right)\right)\)?
    Use the right triangle approach: If \(\theta = \sin^{-1}(-\frac{1}{3})\), then \(\sin \theta = -\frac{1}{3}\). Find adjacent and hypotenuse to calculate \(\cot \theta\).
  • What is the range of the inverse sine function?
    The range of \(\sin^{-1} x\) is \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
  • What is the range of the inverse cosine function?
    The range of \(\cos^{-1} x\) is \([0, \pi]\).
  • What is the range of the inverse tangent function?
    The range of \(\tan^{-1} x\) is \((-\frac{\pi}{2}, \frac{\pi}{2})\).
  • Why are the domains of inverse trig functions restricted?
    To make the trig functions one-to-one and thus invertible, their domains are restricted to intervals where they are monotonic.
  • What is the principal value branch for the inverse sine function?
    The principal value branch for \(\sin^{-1} x\) is \([-\frac{\pi}{2}, \frac{\pi}{2}]\).
  • What is the principal value branch for the inverse cosine function?
    The principal value branch for \(\cos^{-1} x\) is \([0, \pi]\).
  • What is the principal value branch for the inverse tangent function?
    The principal value branch for \(\tan^{-1} x\) is \((-\frac{\pi}{2}, \frac{\pi}{2})\).