(Adding categories) |
m (→Limits: Fixed LaTeX) Tag: Visual edit |
||
Line 35: | Line 35: | ||
===Limits=== |
===Limits=== |
||
− | :<math>\lim_{x\to 0} \frac{sin x}{x} = 1</math> |
+ | :<math>\lim_{x\to 0} \frac{\sin (x)}{x} = 1</math> |
===Approximations=== |
===Approximations=== |
Revision as of 12:51, 29 May 2020
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
If desired, the sine function may be calculated as a direct summation series:
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 . The derivative of is
Trigonometric identities
Sine and cosine can be converted between each other.
Addition of angles under sine:
The sine of an imaginary number becomes a variant of a hyperbolic sine:
The square of sine:
Limits
Approximations
For small values of , there is an easy approximation:
See also
- Cosine
- Cosecant
- Hyperbolic sine
- Law of sines