Arcsine

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 $[-1, 1]$.

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 $y = \arcsin(x)$.

Related terms

Inverse Trigonometric Functions: Functions that reverse the effect of trigonometric functions like sine, cosine, and tangent; includes arcsine, arccosine, and arctangent.

Sine Function: A periodic function defined for all real numbers that calculates the ratio of opposite side to hypotenuse in a right-angled triangle.

Arccosine: The inverse function of cosine, denoted as $\cos^{-1}(x)$ or $\arccos(x)$; returns an angle whose cosine is a given number within [-1, 1].