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Math Help

Under construction - please feel free to add...

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

Google Math!

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