Find two sets of polar coordinates for the point for .
A) ( , )( , )
B) (242, )( 242, )
C) (484, )( 484, )
D) ( , )( , )
E) ( , )( , )

Question

Find two sets of polar coordinates for the point  for  .
A) ( , )( , ) 
B) (242, )( 242, ) 
C) (484, )( 484, ) 
D) ( , )( , ) 
E) ( , )( , )

Quizplus · Accepted Answer

The polar coordinates for a point are given by the distance from the origin to the point (r) and the angle that the line connecting the point to the origin makes with the positive x-axis (θ). The point (11eaa595_6424_935a_a696_bd773c986e8a_TB4584_11_TB4584_11) lies in the third quadrant, so r will be positive and θ will be between 180° and 270°.

The point (11eaa595_6424_935b_a696_a71a19241756_TB4584_11_TB4584_11) is simply a translation of the first point, so it will have the same polar coordinates except that the angle will be increased by 90°. Therefore, the two sets of polar coordinates for this point are:

D) (r, θ) = (484, 225°) and (r, θ) = (484, 315°)

None of the other answer choices provides the correct values for r and θ for this point.

Find Two Sets of Polar Coordinates for the Point