16 terms

how do you sketch a parametric curve

create a table of values with t, x, and y and then graph

MAKE SURE TO SHOW DIRECTION WITH ARROWS from initial point to terminal point

MAKE SURE TO SHOW DIRECTION WITH ARROWS from initial point to terminal point

how to eliminate the parameter

solve for t in one equation and then sub that into the other

what is the equation for a circle centered at zero?

x^2 + y^2 = value

radius = value/2

radius = value/2

how do you eliminate the parameter with an equation involving the square of a cos function plus the square of the sin function?

set cos^2t+ sin^2t=1 equal to x^2 + y^2 =1

what is dy/dx when there is a third variable t

dy/dx= (dy/dt)/(dx/dt) if dx/dt ≠0

formula for arc length l

L= ∫(from α to β) √(dx/dt)² + (dy/dt)² dt

how do you find when the slope of parametric equation is horizontal/vertical

horizontal: find where dy/dx=0, so where dy/dt=0 but dx/dt≠0

vertical : find where dx/dt=0 but dy/dt≠0

vertical : find where dx/dt=0 but dy/dt≠0

what do polar coordinates (r, θ) mean

theta is the angle from the polar axis, r is radius, or how far you go out from center

how do you convert from cartesian/polar and vice versa

use

x=rcosθ

y=rsinθ

x²+y²=r²

y/x=tanθ

x=rcosθ

y=rsinθ

x²+y²=r²

y/x=tanθ

how to sketch polar curves

can make a table of values with theta and r and then plot points

how to find points of intersection of polar equations

draw graphs

set equations equal

solve for thetas

check if pole is on both graphs

set equations equal

solve for thetas

check if pole is on both graphs

area inside a polar curve

a=∫from α to β ½(f(θ))² dθ = ∫from α to β ½(r)² dθ

find area between two polar curves

integral from alpha to beta 1/2 r1 squared - integral 1/2 r2 squared

equation for parabola

x²=4py

y²=4px

*axis of symmetry is axis of degree one variable

*focus: (0,p) or (p,0)

*directrix: y=-p or x=-p

y²=4px

*axis of symmetry is axis of degree one variable

*focus: (0,p) or (p,0)

*directrix: y=-p or x=-p

equation for ellipse

x²/a² + y²/b² = 1

x²/b² + y²/a² = 1

*major axis is on axis of variable with larger denom (a)

*a≥b>0

*c²=a²-b²

*foci determined by c

*major verticies determined by a, minor by b

x²/b² + y²/a² = 1

*major axis is on axis of variable with larger denom (a)

*a≥b>0

*c²=a²-b²

*foci determined by c

*major verticies determined by a, minor by b

equation for hyperbola

x²/a² - y²/b² =1

y²/a² - x²/b² =1

*foci and verts on positive variable's axis

*c²=a²+b²

*verts determined by a

*foci determined by c

*slope of asymptotes: y=a/b or y=b/a

y²/a² - x²/b² =1

*foci and verts on positive variable's axis

*c²=a²+b²

*verts determined by a

*foci determined by c

*slope of asymptotes: y=a/b or y=b/a