a)
To plot: The point with the given rectangular coordinates and find the two sets of corresponding polar coordinates.
a)
Answer to Problem 4E
The rectangular coordinates are shown in Figure (1) and the two sets of corresponding polar coordinates are
Explanation of Solution
Given information: A rectangular coordinate is given as
Formula used:
Let the point P have polar coordinates
The other polar coordinates of P can be calculated as
Calculation:
Plot
Figure (1)
Find the value of
Find the value of
Thus, the corresponding polar coordinate is
Substitute
Substitute
Therefore, the two sets of corresponding polar coordinates are
b)
To plot: The point with the given rectangular coordinates and find the two sets of corresponding polar coordinates.
b)
Answer to Problem 4E
The rectangular coordinates are shown in Figure (2) and the two sets of corresponding polar coordinates are
Explanation of Solution
Given information: A rectangular coordinate is given as
Formula used:
Let the point P have polar coordinates
The other polar coordinates of P can be calculated as
Calculation:
Plot
Figure (2)
Find the value of
Find the value of
Thus, the corresponding polar coordinate is
Substitute
Substitute
Therefore, the two sets of corresponding polar coordinates are
c)
To plot: The point with the given rectangular coordinates and find the two sets of corresponding polar coordinates.
c)
Answer to Problem 4E
The rectangular coordinates are shown in Figure (3) and the two sets of corresponding polar coordinates are
Explanation of Solution
Given information: A rectangular coordinate is given as
Formula used:
Let the point P have polar coordinates
The other polar coordinates of P can be calculated as
Calculation:
Plot
Figure (3)
Find the value of
Find the value of
Thus, the corresponding polar coordinate is
Substitute
Substitute
Therefore, the two sets of corresponding polar coordinates are
d)
To plot: The point with the given rectangular coordinates and find the two sets of corresponding polar coordinates.
d)
Answer to Problem 4E
The rectangular coordinates are shown in Figure (3) and the two sets of corresponding polar coordinates are
Explanation of Solution
Given information: A rectangular coordinate is given as
Formula used:
Let the point P have polar coordinates
The other polar coordinates of P can be calculated as
Calculation:
Plot
Figure (4)
Find the value of
Find the value of
Thus, the corresponding polar coordinate is
Substitute
Substitute
Therefore, the two sets of corresponding polar coordinates are
Chapter 10 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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