Level 535
Level 537

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(r, θ)

polar coordinates

rcosθ

Spherical Polar Coordinates z

rsinθ

converting from rectangular to polar (y)

completing the square

a process used to form a perfect-square trinomial

θ=π/2

symmetry of r=f(sinθ)

Polar Axis

symmetry of r=g(cosθ)

plug in -θ

how to determine symmetry

replace (r,θ) with (-r,-θ)

checking for symmetry to θ=π/2

replace (r,θ) with (r,-θ)

checking for symmetry to polar axis

checking for symmetry to pole

replace (r,θ) with (-r, θ)

r=a±bcosθ (a/b < 1)

limacon with inner loop

Cartioid

r=a±bcosθ (a/b = 1)

dimpled limacon

r=a±bcosθ (1 < a/b < 2)

convex limacon

r=a±bcosθ (a/b > 2)

n petals

rose odd n

2n petals

rose even n

petal length

rose what does a represent

Circle

r=acosθ or r=asinθ

Lemniscate

r²=a²sin2θ or r²=a²cos2θ

Time

D / S

parameter

Number that describes a population

y=3t

equation for a line

y=3/2x

Cartesian equation

Dot product

x times x, y times y, then add them together

c^2=a^2+b^2-2ab*cosC

law of cos

perpendicular

two lines that intersect and form a right angle are

opposite

Two numbers that are an equal distance from zero on a number line; also called additive inverse.

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

multiplying vectors in cross-products

start with terminal-initial to make the chart

other formula

cosx degrees=u*v/absolute value of u times absolute value of v

(x,y)=(x1,y1)+t(slope)

vector equation to use (fill it in)

Distance Formula

absolute value of Aa+Bb+C/square root of A^2+B^2<------those come from the equation, not the point

a+blank(b-a)

find p such that p is blank distance from a to b

find equation perp. to midpoint

find midpoint (those points are x, y, and z), do b-a (those three points are a, b, and c), then do AxByCz, find d, and make the equation

foil the vector equation

to find the parametric equations...

distance b/t point and plane

using the distance formula, plug the point into the plane for the numerator

sas area

A=1/2 ba sinC

aas area

A=1/2 times side^2 sin angle sin angle/sin angle opposite of side given