# 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
```

## 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

### 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