In Exercises 21-26, use a polar coordinate system like the one shown for Exercises 1-10 to plot each point with the given polar coordinates. Then find another representation ( r , θ ) of this point in which a. r > 0 , 2 π < θ < 4 π . b. r < 0 , 0 < θ < 2 π . c. r > 0 , − 2 π < θ < 0. ( 4 , π 2 )
In Exercises 21-26, use a polar coordinate system like the one shown for Exercises 1-10 to plot each point with the given polar coordinates. Then find another representation ( r , θ ) of this point in which a. r > 0 , 2 π < θ < 4 π . b. r < 0 , 0 < θ < 2 π . c. r > 0 , − 2 π < θ < 0. ( 4 , π 2 )
Solution Summary: The author illustrates how the point is (4,pi2) in polar coordinate system.
In Exercises 21-26, use a polar coordinate system like the one shown for Exercises 1-10 to plot each point with the given polar coordinates. Then find another representation
(
r
,
θ
)
of this point in which
a.
r
>
0
,
2
π
<
θ
<
4
π
.
b.
r
<
0
,
0
<
θ
<
2
π
.
c.
r
>
0
,
−
2
π
<
θ
<
0.
(
4
,
π
2
)
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Convert the following polar coordinates into Cartesian coordinates:
3,
6.
a
5,
2
b
(-2,7)e
Which polar coordinate pairs label the same point? a. (-2, π/3) b. (2, -π/3) c. (r, θ) d. (r, θ + π) e. (-r, θ) f. (2, -2π/3) g. (-r, θ + π) h. (-2, 2π/3)
Convert the following Cartesian coordinates into polar coordinates:
(1, 3)e
a
b
(-4, 4)-
(0, 3)е
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Polar Coordinates Basic Introduction, Conversion to Rectangular, How to Plot Points, Negative R Valu; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=aSdaT62ndYE;License: Standard YouTube License, CC-BY