Explanation Given information: The polar coordinate is ( − 5 , − π 6 ) . Explanation: The point P in a polar coordinate system is represented by an ordered pair ( r , θ ) . Here, the point is ( − 5 , − π 6 ) . ⇒ r = − 5 , θ = − π 6 . If P is a point with polar coordinates ( r , θ ) , then the rectangular coordinates ( x , y ) of P are x = r cos θ , y = r sin θ . Therefore, the x -coordinate is x = − 5 cos ( − π 6 ) By using the rule: cos ( − θ ) = cos ( θ ) ⇒ x = − 5 cos ( π 6 ) ⇒ x = − 5 × 3 2 ⇒ x = − 5 3 2

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ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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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.

Chapter 9.1, Problem 51AYU

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The rectangular coordinate of the polar coordinates (−5,−π6).

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Chapter 9.1, Problem 50AYU

Chapter 9.1, Problem 52AYU

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The rectangular coordinate of the polar coordinates ( − 5 , − π 6 ) .

Solution Summary: The author explains the rectangular coordinate of the polar coordinates (-5,-pi6).