Level 639
Level 641

#### 54 words 0 ignored

Ready to learn
Ready to review

## Ignore words

Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.

**Ignore?**

also has a derivative at t.

If f and g have derivatives at t, then the parameterized curve...

(dy/dt)/(dx/dt)

Slope of parameterized curve

(dy¹/dt)/(dx/dt)

Second derivative of parameterized curve

∫√((dx/dt)²+(dy/dt)²)dt

Length of paramterized curve

Surface area of parameterized curve

∫2πy√((dx/dt)²+(dy/dt)²)dt (about x-axis) OR ∫2πx√((dx/dt)²+(dy/dt)²)dt (about y-axis)

Component form of vector

v = <v₁, v₂>

Magnitude of vector

‖v‖ = √(v₁² + v₂²)

<u₁+v₁, u₂+v₂>

Vector addition (u+v)

<u₁-v₁, u₂-v₂>

Vector subraction (u-v)

<ku₁, ku₂>

Scalar multiplication (ku)

Angle between two vectors

cos⁻¹((u₁v₁+u₂v₂)/‖u‖‖v‖ (dot product over product of magnitudes)

Distance

∫|v(t)|dt = ∫√((v₁(t))²+(v₂(t))²)dt

Speed

‖v(t)‖

direction

v(t)/‖v(t)‖ (velocity vector over speed)

rcosθ

Polar x

rsinθ

Polar y

r²

Polar x²+y²

arctan(y/x)

Polar θ

Rose

r=acos(nθ) OR r=asin(nθ)

Lemniscate

r²=a²cos(2θ) OR r²=a²sin(2θ)

limacon

r=a+bcosθ OR r=a+bsinθ

Cartioid

r=a+acosθ OR r=a+asinθ

(r,-θ), (-r,-θ), (-r,θ)

If (r,θ) is on the graph, so are...

it has all three

If a graph has two symmetries...

(rcosθ+r¹sinθ)/(-rsinθ+r¹cosθ)

Slope of polar curve

∫¹/₂r²dθ

Area inside polar curve

¹/₂∫(R²-r²)dθ

Area between two polar curves

∫√((r¹)²+r²)dθ

Length of polar curve

limacon

r = a +/- a sinθ, r = a +/- bcosθ

Y-axis Limacon Equation

r = a +- b sinθ

X-axis Limacon Equation

r = a +- b cosθ

|a| < |b|

There is an inner loop in a limacon if

|a| > |b|

There is NO inner loop in a limacon if

|a| - |b|

Limacons: inner loop or kidney bean shape of what expression

|a| + |b|

Lengthwise distance of Limacon

r = a sin (bθ)

Y-axis symmetric Rose (where b≠1)

r = a cos (bθ)

X-axis symmetric Rose (where b≠1)

Odd

An integer n is defined to be odd if n=2k+1 for some integer k.

Even

An integer n is defined to be even if n=2k for some integer k.

r = a θ

Spirals (θ is in radians)

θ = constant

Line through pole equation

r = constant

Circle with center at pole

Y-axis shifted Circle

r = d sin θ

X-axis shifted Circle

r = d cos θ

|d|

diameter of circle

d>0

circle located on positive side of the axis

d<0

circle located on negative side of the axis

distance formula: between 2 points (r₁, θ₁) and (r₂, θ₂)

d² = r₁² + r₂² - 2 r₁ r₂ cos (θ₂ - θ₁)

circle (general formula)

a² = r₀² + r² - 2 r₀ r cos (θ - θ₀)

r = 2acos(θ-θ₀)

circle through pole

skew lines (not through pole)

d = r cos (θ - α) (or r = d sec (θ - α))

vertical line

r = h sec θ (or rcosθ = h or x = h or r = h/cosθ)

horizontal line

r = k csc θ (or rsinθ = k or y = k or r = k/sinθ)

roses

r = a cos (bθ) r = a sin (bθ)