calc 3 exam 2

Rose Curve

r = asin(n(theta))

r = acos(n(theta)

How do you determine the # of petals on a rose curve?

if n is odd = n petals

if n is even = 2n petals

Area formula in polar coordinates

Power reduction formula

sin²(x) = (1-cos(2x))/2

dy/dx =

(dy/dt)/(dx/dt)

area between curves formula

conversion forumlas from polar to parametric

x = rcos(theta)

y = rsin(theta)

arc length formula for polar coordinates

half angle identity

base terms of a limacon

r = a±bcos

r = a±bsin

Cardioid

a/b = 1

No loop

a > b

Loop

b > a

dimpled

1<a/b<2

Convex

a/b > 2

polor coordinate basic form

(r, θ)

if a polar equation is cosine where is it symmetrical?

horizontal-axis

if a polar equation is sine where is it symmetrical?

vertical axis

is the radius is negative, what direction do you move?

n units up

point slope form

y-y1 = m(x-x1)

standard circle equation

(x-h)² + (y-k)² = r²

||v|| =

sqrt(x² +y² +z²)

projection of one vector onto another =

scalar component

distance formula for planes

point-normal form

parametric equations for a line

if given vertex and focus think:

parabola

if given focus and directrix think:

parabola

if given foci and major axis think:

ellipse

if given foci and vertices and asymptotes think:

hyperbola

if given center and radius think:

circle

one variable squared

parabola

two variables squared and addition

ellipse

two variables squared and subtraction

hyperbola

area of triangle

1/2||u x v||

when given parallelepiped think:

scaler triple product: V = |u . (v x w)|

parametric equations for the tangent line

x= x0 +at and y = y0 +bt

when asked for the distance from a point to a line think:

cross product formula: d = (||AP x v||) / ||v||

angle between two vectors

cos(theta) = (v.w)/||v||||w||

rotation angle forumula

tan(2theta) = B/A-C

when asked for: Express v as the sum of

• a vector parallel to b

• a vector orthogonal to b

projection formula