The sine function $\sin$ is one of the basic functions in trigonometry. It may be thought of as assigning to any angle the distance to a chosen axis of the point on the unit circle with that angle to that axis.
The sine function is the function $\sin \;\colon\; \mathbb{R} \to \mathbb{R}$ from the real numbers to themselves which is characterized by the following equivalent conditions:
$\sin$ is the unique solution among smooth functions to the differential equation/initial value problem
(where a prime indicates the derivative) subject to the initial conditions
(Euler's formula) $\sin$ is the imaginary part of the exponential function with imaginary argument
$\sin$ is the unique function which
is continuous at $0$
satisfies the inequality
and the equation
(see Trimble: Characterization of sine. Some additional discussion at the nForum.)
See at trigonometric identity.
The roots of the sine function, hence the argument where its value is zero, are the integer multiples of pi $\pi \in \mathbb{R}$.
arcsine?
See also
Last revised on November 26, 2017 at 10:54:02. See the history of this page for a list of all contributions to it.