Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with...
Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with −?2<?≤?2−π2<θ≤π2 for the
following Cartesian coordinates:
(a) If (?,?)=(18,−10)(x,y)=(18,−10) then
(?,?)=((r,θ)=( , )),
(b) If (?,?)=(7,8)(x,y)=(7,8) then
(?,?)=((r,θ)=( , )),
(c) If (?,?)=(−10,6)(x,y)=(−10,6) then
(?,?)=((r,θ)=( , )),
(d) If (?,?)=(17,3)(x,y)=(17,3) then
(?,?)=((r,θ)=( , )),
(e) If (?,?)=(−7,−5)(x,y)=(−7,−5) then
(?,?)=((r,θ)=( , )),
(f) If (?,?)=(0,−1)(x,y)=(0,−1) then (?,?)=((r,θ)=( ,))
Plot the point whose spherical coordinates are given. Then find
the rectangular coordinates of the point....
Plot the point whose spherical coordinates are given. Then find
the rectangular coordinates of the point.
(a) (8, π/3, -5)
(x, y, z)
=(_________)
(b) (8, -π/2, 6)
(x, y, z)
= (__________)
Plot the point whose spherical coordinates are given. Then find
the rectangular coordinates of the point....
Plot the point whose spherical coordinates are given. Then find
the rectangular coordinates of the point.
(a) (7, π/3, π/6)
(x,y,z)= (____)
(b) (8, π/2, 3π/4)
(x,y,z)= (____)
Find the rectangular coordinates of the point whose spherical
coordinates are given. (a) (1, 0, 0)...
Find the rectangular coordinates of the point whose spherical
coordinates are given. (a) (1, 0, 0) (x, y, z) = (b) (14, π/3, π/4)
(x, y, z) =
4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =...
4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3,
x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and
yt(3,4)=-100.
Calculate gs(3,4)
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3,
x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and
yt(3,4)=-100.
Calculate gs(3,4)