Inverse sine function

Definition

The inverse sine function, denoted as $\sin^{-1}(x)$ or $\arcsin(x)$, is the inverse operation of the sine function. It returns the angle whose sine value is $x$ within the range $[-\frac{\pi}{2}, \frac{\pi}{2}]$.

5 Must Know Facts For Your Next Test

1. The domain of the inverse sine function is $[-1, 1]$.
2. The range of the inverse sine function is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.
3. The equation $y = \sin^{-1}(x)$ implies that $x = \sin(y)$.
4. Inverse trigonometric functions are used to find angles from given trigonometric ratios.
5. $\arcsin(x)$ is an odd function, meaning $\arcsin(-x) = -\arcsin(x)$.

Review Questions

• What is the domain and range of the inverse sine function?
• How do you express $y = \arcsin(x)$ in terms of a regular sine function?
• Given that $\arcsin(0.5) = y$, what is the value of y?

Related terms

Inverse Cosine Function: Denoted as $\cos^{-1}(x)$ or $\arccos(x)$, it returns the angle whose cosine value is $x$, with a range of $[0, \pi]$.

Inverse Tangent Function: Denoted as $\tan^{-1}(x)$ or $\arctan(x)$, it returns the angle whose tangent value is $x$, with a range of $\left(-\frac{\pi}{2}, \frac{3\pi}{2}\right)$.

Periodic Functions: $A periodic function repeats its values in regular intervals or periods.$