sin(x), sine function.
Sine definition
In a right triangle ABC the sine of α, sin(α) is defined as the ratio betwween the side opposite to angle α and the side opposite to the right angle (hypotenuse):
sin α = a / c
Example
a = 3"
c = 5"
sin α = a / c = 3 / 5 = 0.6
Graph of sine
TBD
Sine rules
Rule name | Rule |
---|---|
Symmetry | sin(-θ) = -sin θ |
Symmetry | sin(90°- θ) = cos θ |
Pythagorean identity | sin^{2} α + cos^{2} α = 1 |
sin θ = cos θ × tan θ | |
sin θ = 1 / csc θ | |
Double angle | sin 2θ = 2 sin θ cos θ |
Angles sum | sin(α+β) = sin α cos β + cos α sin β |
Angles difference | sin(α-β) = sin α cos β - cos α sin β |
Sum to product | sin α + sin β = 2 sin [(α+β)/2] cos [(α-β)/2] |
Difference to product | sin α - sin β = 2 sin [(α-β)/2] cos [(α+β)/2] |
Law of sines | a / sin α = b / sin β = c / sin γ |
Derivative | sin' x = cos x |
Integral | ∫ sin x dx = - cos x + C |
Euler's formula | sin x = (e^{ix} - e^{-ix}) / 2i |
Inverse sine function
The arcsine of x is defined as the inverse sine function of x when -1≤x≤1.
When the sine of y is equal to x:
sin y = x
Then the arcsine of x is equal to the inverse sine function of x, which is equal to y:
arcsin x = sin^{-1}(x) = y
See: Arcsin function
Sine table
x (°) |
x (rad) |
sin x |
---|---|---|
-90° | -π/2 | -1 |
-60° | -π/3 | -√3/2 |
-45° | -π/4 | -√2/2 |
-30° | -π/6 | -1/2 |
0° | 0 | 0 |
30° | π/6 | 1/2 |
45° | π/4 | √2/2 |
60° | π/3 | √3/2 |
90° | π/2 | 1 |
Currently, we have around 929 calculators and conversion tables to help you "do the math" quickly in areas such as:
- Free online calculators and tools
- Free online units conversion tools
- Free online web design tools
- Free online electricity & electronics tools
- Mathematics
- Online tool
- Text tool
- PDF tool
- Code
- Ecology
- Numbers
- Algebra
- Trigonometry
- Probability & Statistics
- Calculus & analysis
- Mathematical symbols
- Cosine function
- Sine function
- Tangent function
- Arccos(x) function
- Arccos of 0
- Arccos of 1
- Arccos of 2
- Arccos of 3
- Arccos of cos(x)
- Arccos of sin(x)
- Arccos(x) derivative
- Arccos(x) graph
- Cos of arccos(x)
- Sin of arccos(x)
- Tan of arccos(x)
- Arcsine function
- Arcsin of 0
- Arcsin of 1
- Arcsin of infinity
- Arcsin graph
- Arcsin derivative
- Arcsin integral
- Sin of arcsin
- Cos of arcsin
- Tan of arcsin
- Arctangent function
- Arctan of 0
- Arctan of 1
- Arctan of 2
- Arctan of infinity
- Derivative of arctan
- Integral of arctan
- sine of arctan(x)
- Cosine of arctan(x)
- Arctan graph
And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.
Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.