Question

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)

Answer 1

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)