No edit summary Tag: rte-source |
m (→Properties) Tag: sourceedit |
||
Line 8: | Line 8: | ||
As a result of [[Euler's formula]], the sine function can also be represented as |
As a result of [[Euler's formula]], the sine function can also be represented as |
||
− | :<math>\sin(\theta)=\frac{e^{\theta i}-e^{-\theta i}}{ |
+ | :<math>\sin(\theta)=\frac{e^{\theta i}-e^{-\theta i}}{2i}</math> |
The [[reciprocal]] of sine is [[cosecant]] (abbreviated as <math>\csc</math>), while its inverse is <math>\arcsin</math> or <math>\sin^{-1}</math> . Note that sine is not being raised to the [[exponentiation|power]] of -1; this is an [[inverse function]], not a reciprocal. |
The [[reciprocal]] of sine is [[cosecant]] (abbreviated as <math>\csc</math>), while its inverse is <math>\arcsin</math> or <math>\sin^{-1}</math> . Note that sine is not being raised to the [[exponentiation|power]] of -1; this is an [[inverse function]], not a reciprocal. |
Revision as of 03:36, 2 February 2017
Sine () is a trigonometric ratio. In a right triangle with an angle ,
is the side of the triangle facing(opposite to) angle , and 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
The reciprocal of sine is cosecant (abbreviated as ), while its inverse is or . Note that sine is not being raised to the power of -1; this is an inverse function, not a reciprocal.
The derivative of is , while its antiderivative is .