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

then plot the point.

(a) (5, 7π/4)

(r, θ) ( ) (r > 0)
(r, θ) ( ) (r < 0)

(b) (−6, π/2)

(r, θ) ( ) (r > 0)
(r, θ) ( ) (r < 0)

(c) (5, −2)

(r, θ) ( ) (r > 0)
(r, θ) ( ) (r < 0)

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)

she will sew have sewn five dresses   and be 1/3 done with the sixth one in an hour.

step-by-step explanation:

3/4 of an hour=45 mins

lucy makes 1 dress per 11.25 minutes

45 mins+11.25 mins=56.25 mins

60 mins- 56.25 mins=3.75 mins

3.75 mins is 1/3 of of 11.25 mins

therefore she the other 1/3 would be part of the hour and she will have sewn 5 dresses and begun the sixth.

contact me if you have any questions you are welcome.