Concept Check Fill in the blank to correctly complete each sentence. The point (−1, 3) lies in quadrant ________ in the rectangular coordinate system .

Question

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Answer 1

Textbook Question

Chapter B, Problem 1E

Concept Check Fill in the blank to correctly complete each sentence.

The point (−1, 3) lies in quadrant ________ in the rectangular coordinate system.

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.

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

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Answer 2

Textbook Question

Chapter B, Problem 1E

Concept Check Fill in the blank to correctly complete each sentence.

The point (−1, 3) lies in quadrant ________ in the rectangular coordinate system.

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.

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

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Answer 3

Textbook Question

Chapter B, Problem 1E

Concept Check Fill in the blank to correctly complete each sentence.

The point (−1, 3) lies in quadrant ________ in the rectangular coordinate system.

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.

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

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Answer 4

Textbook Question

Chapter B, Problem 1E

Concept Check Fill in the blank to correctly complete each sentence.

The point (−1, 3) lies in quadrant ________ in the rectangular coordinate system.

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.

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

Answer 8

Expert Solution & Answer

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.

Therefore, the point (−1,3) is (−x,+y) type and lies in the second quadrant.

The graph is as follows:

Trigonometry (11th Edition), Chapter B, Problem 1E

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

To fill: The blank of the statement, “The point (−1,3) lies in quadrant __ in the rectangular co-ordinate system.”

Answer 12

Answer to Problem 1E

Solution: The point (−1,3) lies in quadrant second in the rectangular co-ordinate system.

Answer 13

Explanation of Solution

The rectangular co-ordinate system is divided into four quadrants. The point’s (+x,+y) type lies in the first quadrant. The point’s (−x,+y) type lies in the second quadrant. The point’s (−x,−y) type lies in the third quadrant. The point’s (+x,−y) type lies in the fourth quadrant.