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The
sine function is an
elementary transcendental function. The
sine of an angle
, denoted as
, is one of the most important [circular]
trigonometric functions.
Given the angle
of an arc on a
unit circle,
is the length of the side on a right triangle opposing a vertex coinciding with the center of the circle (the other two sides of the triangle being the hypotenuse and a side that is a line along
).
- (PLACEHOLDER FOR IMAGE) [1]
Per the
Pythagorean theorem,
(sin θ ) 2 + (cos θ ) 2 = 1 |
, usually written
(where
, i.e. not the sine of the sine of
).
The graph of the sine function has given rise to the term “sine wave” to distinguish between sinuous waves that look like this
(sine is in red, cosine in blue) and sawtooth and triangular waves.
Table of sine and cosine values
For the decimal expansions of the sine from 1 to 89 degrees, see
A019810 through
A019898 (with the
A-number being given by 19809 plus the desired number of degrees between 1 and 89—except for 30, 45 and 60 degrees). In the following table,
, and all non-integral values are given to 8 decimal places (click the link for the sequence entry for far greater precision).
Taylor series expansion
The Taylor series expansion of the sine function is
-
sin x = x 2 n + 1 = x − + − + ⋯. |
Formulae
(...)
See also
- {{sin}} mathematical function template
Notes