essential math formulas

Law of sine

Law of Cosine

c	=	length of side c
a	=	length of side a
c	=	length of side b
γ	=	angle opposite c

combinations formula (order does not matter), for combination with k number of items, and n sized groupings

k!/n!*(k-n)!

permutations formula (order does matter), for permutations of k sized collection, and n sized groupings

k!/(k-n)!

formula for finding sum of arithmetic series

(final+initial/2)*number of terms

limits of law of sine

can only be used to determine acute angles

triangle area formula (universally acceptable)

A=1/2*a*b*sinC

geometric sequence sum formula

S=(first-last*multiplier)/(1-multiplier)

extended law of sines

(a/sina)=diameter of circumcircle

double angle formula for sine

sin2A =2sinAcosA

double angle formula for cosine

cos2A=cos²A-sin²A

cos2A=2cos²A-1

midpoint formula

((x₁+x₂)/2, (y₁+y₂)/2)

distance formula

√((x₁-x₂)²+(y₁-y₂)²)

general parametric equation for a circle

(x+rcosA, y+rsinA)

abs val rules

if unrooting even roots, abs val both sides, or which ever is being rooted

if log term is squared

treat problem as quadratic

domain of sin-1 and cos-1 funcs

[-1,1]

Heron’s Formula

1/4*√((a+b+c)*(a+b-c)*(a-b+c)*(-a+b+c))

sinß+∂

sinßcos∂ + sin∂cosß

cosß+∂

cosßcos∂-sinßsin∂

sinß-∂

sinßcos∂ - sin∂cosß

cosß-∂

cosßcos∂+sinßsin∂

tanß+∂

(tan∂ + tanß)/(1-tanßtan∂)

Remainder theorem

when polynomial P(x) is divided by (x-a), then the remainder is P(a). (the divisor MUST be linear)