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)=( ,))
1.
Convert the Cartesian coordinates of (122m,10m) to polar
coordinates.
A. (11.49m, 4.69°) B. (122.4m, 4.69°)...
1.
Convert the Cartesian coordinates of (122m,10m) to polar
coordinates.
A. (11.49m, 4.69°) B. (122.4m, 4.69°) C. (122.4m, 85.3°) D.
(11.49m, 85.3°)
2. Convert the polar coordinates of (135m, 182°) to Cartesian
coordinates
A. (-4.71m, 134.9m) B. (134.9m, 4.71m) C. (-134.9m, -4.71m) D.
(4.71m, 134.9m)
3. A Basketball player shoots from beyond the 3-point arc. The
ball leaves the band with an initial velocity of 8m/s angled 52°
from the horizontal. What are the horizontal and vertical
velocities of the...
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 <...
1) Sketch the graph?=? ,?=? +3,and include orientation.
2) Sketch the graph ? = sin ?...
1) Sketch the graph?=? ,?=? +3,and include orientation.
2) Sketch the graph ? = sin ? , ? = sin2 ? + 3 and include
orientation.
3) Remove the parameter for ? = ? − 3, ? = ?2 + 3? − 2 and write
the corresponding
rectangular equation.
4) Remove the parameter for ? = 2 + 3 sin ? , ? = −1 + 3 cos ?
and write the corresponding rectangular equation.
5) Create a parameterization for...
a) Find the parametric equations for the circle centered at
(1,0) of radius 2 generated clockwise...
a) Find the parametric equations for the circle centered at
(1,0) of radius 2 generated clockwise starting from
(1+21/2 , 21/2). <---( one plus square
root 2, square root 2)
b) When given x(t) = tcost, y(t) = sint, 0 <_ t. Find dy/dx
as a function of t.
c) When given the parametric equations x(t) =
eatsin2*(pi)*t, y(t) = eatcos2*(pi)*t where a
is a real number. Find the arc length as a function of a for 0
<_ t...