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Level 536

Parametric Equations


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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