Polar coordinates?

Which of the following is NOT the same point in polar coordinates as (3, -1.236)?
(-3, 1.906)
(3, -7.518)
(3, 5.047)
(-3, 1.236)

1 Answer
Jan 30, 2018

All the three are different from (-3, 1.236)

Explanation:

r = sqrt(x^y + y^2), theta = tan ^(-1) (y/x)

Polar coordinates for
1. (-3, 1.906)

#r = sqrt((-3)^2 + (1.906)^2) ~~ 3.5543#

#theta = tan (-1) (1.906/-3) ~~ -43.4292^0#

  1. (3, -7.518)

#r = sqrt((3)^2 + (-7.518)^2) ~~ 8.0945#

#theta = tan (-1) (-7.518/3) ~~ --68.2459^0#

  1. ( 3, 5.047)

#r = sqrt((3)^2 + (5.047^2) ~~ 5.8713#

#theta = tan (-1) (5.047/3) ~~ -59.2722^0#

  1. (-3, 1.236)

#r = sqrt((-3)^2 + (1.236)^2) ~~ 3.2446#

#theta = tan (-1) (1.236/-3) ~~ -22.3917^0#

  1. (-3, 1.906) #r ~~ 3.5543#, #theta) ~~ -43.4292^0#

  2. (3, -7.518) #r ~~ 8.0945#, #theta ~~ --68.2459^0#

  3. ( 3, 5.047) #r ~~ 5.8713#, #theta ~~ -59.2722^0#

  4. (-3, 1.236) #r ~~ 3.2446#, #theta ~~ -22.3917^0#

All the three are different from (-3, 1.236)