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)=( ,))
The Cartesian coordinates of a point are given. (a) (−3, 3)
(i) Find polar coordinates (r,...
The Cartesian coordinates of a point are given. (a) (−3, 3)
(i) Find polar coordinates (r, θ) of the point, where r > 0
and 0 ≤ θ < 2π.
(r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where r < 0
and 0 ≤ θ < 2π.
(r, θ) =
(b) (4, 4 sq root3 ) (i) Find polar coordinates (r, θ) of the
point, where r > 0 and 0 ≤ θ < 2π....
The Cartesian coordinates of a point are given.
(a) (5
3
, 5)(i) Find polar coordinates (r,...
The Cartesian coordinates of a point are given.
(a) (5
3
, 5)(i) Find polar coordinates (r, θ) of the point,
where
r > 0 and 0 ≤ θ < 2π.
(r, θ) =
(ii) Find polar coordinates (r, θ) of the point, where
r < 0 and 0 ≤ θ < 2π.
(r, θ) =
(b)
(1, −3)
(i) Find polar coordinates (r, θ) of the point,
where
r > 0 and 0 ≤ θ <...
The Cartesian coordinates of a point are given. (a) (−4, 4) (i)
Find polar coordinates (r,...
The Cartesian coordinates of a point are given. (a) (−4, 4) (i)
Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤
θ < 2π. (r, θ) (ii) Find polar coordinates (r, θ) of the point,
where r < 0 and 0 ≤ θ < 2π. (r, θ) (b) (3, 3 3 ) (i) Find
polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ
< 2π. (r, θ) =...
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...
The Cartesian coordinates of a point are given.
(a) (−8, 8)
(i) Find polar coordinates...
The Cartesian coordinates of a point are given.
(a) (−8, 8)
(i) Find polar coordinates
(r, θ) of the point, where
r > 0 and 0 ≤ θ < 2π.
(ii) Find polar coordinates
(r, θ) of the point, where
r < 0 and 0 ≤ θ < 2π.
(b) (4,4sqrt(3))
(i) Find polar coordinates
(r, θ) of the point, where
r > 0 and 0 ≤ θ < 2π.
(ii) Find polar coordinates (r, θ)...