Changes: Sine

Revision as of 08:55, 10 March 2015

Sine ( $\sin$ ) is a trigonometric ratio. In a right triangle with an angle $\theta$ ,
$\sin \theta ={\frac {\mbox{opposite}}{\mbox{hypotenuse}}}$
$\text{Opposite}$ is the side of the triangle facing(opposite to) angle $\theta$ , and $\text{hypotenuse}$ is the side opposite the right angle.

Properties

The sine of an angle is the y-coordinate of the point of intersection of said angle and a unit circle.

As a result of Euler's formula, the sine function can also be represented as

\sin(\theta )={\frac {e^{i\cdot \theta }-e^{-i\cdot \theta }}{2}}

The reciprocal of sine is cosecant (abbreviated as $\csc$ ), while its inverse is $\arcsin$ or $\sin^{-1}$ . Note that sine is not being raised to the power of -1; this is an inverse function, not a reciprocal.

The derivative of $\sin(x)$ is $\cos(x)$ , while its antiderivative is $-\cos(x)$ .

This trigonometry-related article contains minimal information concerning its topic. You can help the Mathematics Wikia by adding to it.

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 '''Sine''' (<math>\sin</math>) is a [[Trigonometry|trigonometric]] ratio. In a [[right triangle]] with an angle <math>\theta</math>,<br/>
 <math>\sin\theta=\frac{\mbox{opposite}}{\mbox{hypotenuse}}</math><br/>
-<math>\text{Opposite}</math> is the side of the triangle not part of angle <math>\theta</math>, and <math>\text{hypotenuse}</math> is the side opposite the [[right angle]].
+<math>\text{Opposite}</math> is the side of the triangle facing(opposite to) angle <math>\theta</math>, and <math>\text{hypotenuse}</math> is the side opposite the [[right angle]].
 ==Properties==