Precalc Ch. 5,8,9,10

x in polar form

rcostheta

y in polar form

rsintheta

(y-k)² =4a(x-h)

parabola that opens right

(y-k)² =-4a(x-h)

parabola that opens left

(x-h)² =4a(y-k)

parabola that opens up

(x-h)² =-4a(y-k)

parabola that opens down

a² =b² +c²

components of ellipse

c² =a² +b²

components of hyperbola

y=(b/a)x

asymptote of hyperbola with transverse along x

y=(a/b)x

asymptote of hyperbola with transverse along y

r=ep/1+ecostheta

directrix perpendicular, p units to the right

r=ep/1-ecostheta

directrix perpendicular, p units to the left

r=ep/1+esintheta

directrix parallel, p units above

r=ep/1-esintheta

directrix parallel, p units below

B² -4AC=0

parabola

B² -4AC<0

Ellipse

B² -4AC>0

Hyperbola

x’cos-y’sin

rotation for x

x’sin+y’cos

rotation for y

32ft/sec² ; 9.8m/sec²

g constant of acceleration

c/a

eccentricity

r=a+-acosθ

Cardioid

r=a+-asinθ

Cardioid

r=a+-bsinθ

Limacon

r=a+-bcosθ

Limacon

Limacon without loop

a>b

Limacon with loop

a<b

r² =a²sin(2θ)

Lemniscate

r² =a²cos(2θ)

Lemniscate

r=acos(nθ)

Rose

r=asin(nθ)

Rose

rcosθ=a

line

rsinθ=a

line

r=a

circle

r=acosθ

circle

r=asinθ

circle

r=2-2sinθ

cardioid

r=2-3cosθ

limacon w/inner loop

r=3-2cosθ

limacon w/o inner loop

r²=4cos(2θ)

lemniscate

r=2cos(3θ)

rose

rsinθ=4

line

r=2cosθ

circle

ambiguous case

SSA

A=sqrt[s(s-a)(s-b)(s-c)]

Heron’s Formula

1/2ba(singamma)

Area formula

loga(1/N)

-logaN

cosacosb+sinasinb

cos(a-b)

sinacosb-sinbcosa

sin(a-b)

replace theta with -theta

polar axis symmetry test

replace theta with pi-theta

theta=pi/2 symmetry test

replace r with -r

pole symmetry test

rⁿ[cos(ntheta)+isin(ntheta)]

DeMoivre’s Theorem

r^1/n [cos(theta/n +2kpi/n)+isin(theta/n +2kpi/n)]

Complex Roots Theorem

z=r(costheta + isintheta)

Polar Form

r₁r₂[cos(theta₁+theta₂)+isin(theta₁+theta₂)]

z₁z₂

r_1/r₂[cos(theta₁-theta₂)+isin(theta₁-theta₂)]

z₁/z₂

(a₁+a₂)i+(b₁+b₂)j

v+w

(a₁-a₂)i+(b₁-b₂)j

v-w

sqrt (a²+b²)

magnitude v

v/||v||

unit vector

a₁i+b₁j

v

a₂i+b₂j

w

(v₀costheta)t

projectile motion x

-1/2gt²+(v₀sintheta)t+h

projectile motion y