Circle:

Circumference of circle = 2πR

Pi is also known as Archimedes’ constant

Radians:

2π = 360 degrees

1 = 57 degrees

Area, A = πR^2

Sphere:

Surface Area, S = 4 πR^2

Volume, V = 4/3 πR^3

Trigonometry:

c b

a

Sin(a,c) = b/c

Cos(a,c) = a/c

Tan(a,c) = b/a = sin(a,c)/cos(a,c)

Important approximations for very small (<1degrees) angles (in units of radians):

Sin(a,c) = a,c

Cos(a,c) = 1

Tan(a,c) = a,c

Exponential Function:

f(x) = a^x

a = 2 (1,2,4,8,…)

Exponential Decay:

f(x) = a^-x

a = 2 (1, ½, ¼, …)

Logarithmic Functions:

f(x) = log(a,x)

log(a,a^x) = x

Most important bases: a=10 (decadic logarithm), a=e 2.71828… (natural logarithm)

Periodic Functions:

Use Sin and Cos to express periodic functions

Sin(alpha) = sin(alpha+360) = sin(alpha+2π)

Cos(alpha) = cos(alpha+360) = cos(alpha+2π)

Sin^2(alpha) + cos^2(alpha) = 1

Sin Graph

Cos Graph

Coordinates and Vectors

y

Y2 2

Y1 1

X1 X2 X

Point 1: (x1,y1) (vertical bracket)

Point 2: (x2,y2)

(xd, yd) = (x2,y2) – (x1,y1)

Distance, d = SQUAREROOT(xd^2 + yd^2), = SQUAREROOT(x2-x1)^2 + (y2-y1)^2

Basic Statistics:

Assumption: set of N numbers, (x1,x2,x3….xn)

Mean = 1/n (x1+x2+x3…+xn) or 1/n SUM(from 1 to N)(xi)

Standard Deviation (scatter) = SQUAREROOT(1/N * SUM(from 1 to N)(xi-xmean)^2)