Question

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)=( ,))

Answer #1

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) (−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) (−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) =...

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)...

given the polar curve r = 2(1+cos theta) find the Cartesian
coordinates (x,y) of the point of the curve when theta = pi/2 and
find the slope of the tangent line to this polar curve at theta =
pi/2

Position and velocity of a point are given in polar coordinates
by R = 2, θ = 35 degrees, and
v = 4R + 3Θ. The 35
degrees is measured positive counterclockwise from the
x-axis on an xy Cartesian coordinate frame. What
is the velocity of the point in terms of i and
j?

My Notes
Ask Your Teacher
Find the Cartesian coordinates of the given polar coordinates.
Then plot the point.(a)
(4, π)
(x, y) =
(b)
(4, −2π/3)
(x, y) =
(c)
(−4, 3π/4)
(x, y) =

1. You are given the point P in the cartesian coordinates (−4,
−4). Write the point in polar coordinates given the
restrictions:
(a) r > 0, and 0 ≤ θ < 2π. (in these programs, r = 0 is
just defined to be the origin).
(b) r<0andθ∈[0,2π)
(c) Write the point in polar coordinates that represent the
same point P but that
is different than the previous parts.

Solve the given nonlinear plane autonomous system by changing to
polar coordinates.
x'
=
−y − x(x2 + y2)2
y'
=
x − y(x2 +
y2)2, X(0) = (3, 0)
(r(t), θ(t)) =

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...

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