ch 10 Flashcards
how to find tangent line to parametric curve
find dy/dx
plug in x or y to solve for t
cancel t’s by plugging it into x or y equation
plug t into dy/dx equation and write in y=mix+b
parabola
one squared
circe=le
exactly the same
ellipse
same sign but different h
hyperbola
different signs
area of a parametric curve
s = sqrt (dx/dt)^2 + (dy/dt)^2
polar to rectangular
rcostheta, rsintheta
rectangular to polar
(+- sqrt x^2+y^2, arctan(y/x))
find value on theta w point on curve with shortest distance from pole
find dr/dtheta
and set = 0
find critical points and use that and end points
plug everything into r and see shortest
area of a sector
a = 1/2 int r^2dr
circle equation
r=asintheta r=acostheta
cardioid equation and features
r= a+_bcostheta
r=a+_bsintheta
heart shaped
a/b=1
limacon w inner loop
r=a+_ bcostheta
r=a+_bsintheta
inner loop
a/b <1
dimpled limacon
r=a+_bcostheta
1<a/b<2
convex limacon
a/b>2
rose curves
r=acosbtheta
lemniscate
r^2 = a^2sin2theta
finding tangent to polar curve
equation
dy/dx =
(r’thetasintheta + rthetacostheta)
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(r’thetacostheta + r theta sin theta)
x = rcostheta. y = rsintheta
tangent at the pole
dy/dx = tan theta
arc length of polar curve
s = int sqrt (theta)^2 + f’theta^2
