# Math Help

Under construction - please feel free to add...

The best calculator available on the net is the Google search box!

For example if you enter:

c in furlongs/fortnight

It will give you the speed of light in the most esorteric dimensions imaginable.

the speed of light = 1.8026175 × 10^12 furlongs / fortnight

## Contents

## Math Links

## Simple Trigonometry

It is helpful to read equations aloud until you have some experience with them. Here is a guide on how to pronounce different equations.

- sin(θ) is read as "the sine of Theta".
- cos(θ) is read as "the cosine of Theta".
- tan(θ) is read as "the tangent of Theta".

In a right triangle the:

- sin(θ)=opposite/hypotenuse or a/c
- cos(θ)=adjacent/hypotenuse or b/c
- tan(θ)=opposite/adjacent a/b

### Pythagorean Theorem

a^2+b^2=c^2 - Read as a squared plus b squared equals c squared.

The Pythagorean Therom is used to find an unknown side length if the other two are known in a right triangle.

### Angle Theorem

The sum of all angles in a triangle are equal to 180 degrees.

### Examples

With sin, cos, tan and the Pythagorean Theorem you can solve all of the sides and angles in a right triangle if any 3 parameters are known.

For Example:

If a=7 and b=5 then

7^2+5^2=c^2

49+25=c^2

74=c^2

sqr(74)=c

8.6=c

Now we have all three sides.

sin(θ)=7/8.6

sin(θ)=.814

θ=arcsin(.814) - Pronounced theta equals the arc sine of point 814.

θ=54.5deg

Now we have two angles (90 and 54.5):

180=90+54.5+(our missing angle)

180-90-54.5=our missing angle

our missing angle = 35.5.

Now we have solved all of the sides and angles of this right triangle. I choose to use Pythagorean Theorem, sin and the angle theorem but we could have used other choices.

### Simple Identities

- tan(θ) = sin(θ) / cos(θ) = a / b
- sin(-θ) = -sin(θ)
- cos(-θ) = cos(θ)
- tan(-θ) = -tan(θ)
- sin^2(θ) + cos^2(θ) = 1

- sin(2x) = 2 sin x cos x
- cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x)
- tan(2x) = 2 tan(x) / (1 - tan^2(x))
- sin^2(x) = 1/2 - 1/2 cos(2x)
- cos^2(x) = 1/2 + 1/2 cos(2x)
- sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )
- cos x - cos y = -2 sin( (x-y)/2 ) sin( (x + y)/2 )

### Law of Sines

Given Triangle abc, with angles A,B,C; a is opposite to A, b oppositite B, c opposite C:

a/sin(A) = b/sin(B) = c/sin(C)

### Law of Cosines

- c^2 = a^2 + b^2 - 2ab cos(C)
- b^2 = a^2 + c^2 - 2ac cos(B)
- a^2 = b^2 + c^2 - 2bc cos(A)

### Law of Tangents

- (a - b)/(a + b) = tan 1/2(A-B) / tan 1/2(A+B)

## The Greek Alphabet

- Α - Alpha
- α - Alpha Lower Case
- Β - Beta
- β - Beta Lower Case
- Γ - Gama
- γ - Gama Lower Case
- Δ - Delta - Sometimes spoken as "the change in".
- δ - Delta Lower Case
- Ε - Epsilon
- ε - Epsilon Lower Case
- Ζ - Zeta
- ζ - Zeta Lower Case
- Η - Eta
- η - Eta Lower Case
- Θ - Theta
- θ - Thete Lower Case - Used to represent angles.
- Ι - Iota
- ι - Iota Lower Case
- Κ - Kappa
- κ - Kappa Lower Case
- Λ - Lamda
- λ - Lamda Lower Case - Used to represent wavelength.
- Μ - Mu
- μ - Mu Lower Case
- Ν - Nu
- ν - Nu Lower Case
- Ξ - Xi
- ξ - Xi Lower Case
- Ο - Omicron
- ο - Omicron Lower Case
- Π - Pi
- π - Pi Lower Case - The diameter of a circle divided by it's diameter
- Ρ - Rho
- ρ - Rho Lower Case
- Σ - Sigma - "The sum of"
- σ - Sigma Lower Case
- ς - Sigma
- Τ - Tau
- τ - Tau Lower Case
- Υ - Upsilon
- υ - Upsilon Lower Case
- Φ - Phi
- φ - Phi Lower Case
- Χ - Chi
- χ - Chi Lower Case
- Ψ - Psi
- ψ - Psi Lower Case
- Ω - Omega
- ω - Omega Lower Case