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Arcsine

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Algebra and Trigonometry

Definition

Arcsine is the inverse function of the sine function, denoted as $\sin^{-1}(x)$ or $\arcsin(x)$. It returns the angle whose sine is a given number within the range of $[-1, 1]$.

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5 Must Know Facts For Your Next Test

  1. Arcsine function outputs angles in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
  2. The domain of arcsine is $[-1, 1]$, meaning it only accepts values within this range.
  3. If $y = \arcsin(x)$, then $\sin(y) = x$ for $x$ in the domain and $y$ in the range of arcsine.
  4. The derivative of arcsine with respect to x is $\frac{d}{dx} (\arcsin(x)) = \frac{1}{\sqrt{1-x^2}}$.
  5. In trigonometric identities, arcsine can be used to solve equations involving sine by isolating the variable.

Review Questions

  • What is the range of the arcsine function?
  • If $\arcsin(0.5) = y$, what is the value of y?
  • Calculate the derivative of $y = \arcsin(x)$.
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