Question

Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0.

Answer 1

Answer:

A) (5, 7π/4):   (5, 15π/4) and (-5, 3π/4)

B) (−6, π/2):   (−6, 5π/2) and (6, -π/2)

C) (5, −2):       (5, 2π-2) and (-5, -π-2)

Step-by-step explanation:

To find pair of coordinates for (r>0), add 2π to corresponding θ. For (r<0) subtract π from given angle to find second pair of coordinate.

A)  (5, 7π/4)

For (r>0)

θ =  7π/4 + 2π

θ =  15π/4

Point is (5, 15π/4)

For (r<0)

θ =  7π/4 - π

θ =  3π/4

Point is (-5, 3π/4)

As it can be seen in Fig 1

(5, 7π/4)=(5, 15π/4)=(-5, 3π/4)

B)  (−6, π/2)

For (r>0)

θ =  π/2 + 2π

θ =  5π/2

Point is (6, 5π/2)

For (r<0)

θ =  π/2 - π

θ =  -π/2

Point is (-6, -π/2)

As shown in fig 2

(-6, π/2) = (6, 5π/2) = (-6, -π/2)

C) (5, −2)

For (r>0)

θ =  -2 + 2π

Point is (5, 2π-2)

For (r<0)

θ =  -2 - π

Point is (-5, -π)

As shown in Fig. 3

(5, −2) = (5, 2π-2) = (-5, -π)