Use the following ?gure as an aid in identifying the relationship between the rectangular, cylindrical, and spherical coordinate systems. For the following exercises, the cylindrical coordinates ( r , θ , z ) of a point are given. Find the rectangular coordinates ( x , y , z ) of the point. 363. ( 4 , π 6 , 3 )
Use the following ?gure as an aid in identifying the relationship between the rectangular, cylindrical, and spherical coordinate systems. For the following exercises, the cylindrical coordinates ( r , θ , z ) of a point are given. Find the rectangular coordinates ( x , y , z ) of the point. 363. ( 4 , π 6 , 3 )
Use the following ?gure as an aid in identifying the relationship between the rectangular, cylindrical, and spherical coordinate systems.
For the following exercises, the cylindrical coordinates
(
r
,
θ
,
z
)
of a point are given. Find the rectangular coordinates
(
x
,
y
,
z
)
of the point.
363.
(
4
,
π
6
,
3
)
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.
A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counterclockwise. What are the coordinates of the child after 120 seconds?
A child enters a carousel that takes one minute to revolve once around. The child enters at the point
(0, 1), that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 60 seconds?
Enter the exact answer as a point, (a, b).
Ay
A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1), that is, on the due north position. Assume the carousel revolves counterclockwise.
What are the coordinates of the child after 15 seconds?
Enter the exact answer as a point, (a,b).
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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