Question

(1 point) Convert the following polar coordinates into
rectangular coordinates.

(a) 〈2∠45∘〉

x= _____, y= _____.

(b) 〈4∠120∘〉

x= _____, y= _____.

(c) 〈6∠270∘〉

x= _____, y= _____.

(d) 〈6∠300∘〉

x= _____, y= _____.

Answer #1

Solution

a)

b)

c)

d)

convert (2,-25 degrees) into rectangular coordinates from polar
coordinates

(1 point)
Convert the following point from rectangular to cylindrical
coordinates:
(4√2,−4√2,9)
(r,θ,z)=

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.
(a) (7, π/3, π/6)
(x,y,z)= (____)
(b) (8, π/2, 3π/4)
(x,y,z)= (____)

1. Convert y^2 =9x into to the full polar coordinates. Show
work.
2. Solve the differential equation with the given initial
condition. dy/dx = (xsinx)/y when y(0)=-1
Thank you.

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)
= (__________)

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

1) Convert the point (x,y,z)=(−2,5,3) to spherical coordinates.
Give answers as positive values, either as expressions, or decimals
to one decimal place.
(ρ,θ,ϕ)=
2) Convert the point (r,θ,z)=(2,2π,4) to Cartesian coordinates.
Give answers either as expressions, or decimals to at least one
decimal place.
(x,y,z)=
3) Convert the point (ρ,θ,ϕ)= (5,5π/3,3π/4) to Cartesian
coordinates. Give answers either as expressions, or decimals to at
least one decimal place.
(x,y,z) =

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) =

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...

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