Question

Determine two pairs of polar coordinates for (-3,0) when . a. (3,180°), (-3,0°) c. (3,0°), (-3,180°) b. (3,270°), (-3,90°) d. (3,90°), (-3,270°) Please select the best answer from the choices provided A B C D

Answer 1

Given: The points ( x,y) = (-3,0)

To find: The corresponding polar coordinates?

Solution:

• First we need to find the r by the formula:

           r = √x² + y²

           r = √(-3)² + 0²

          r = 3

• Now to find the value of α, we have:

          α = tan^-1 { mod (y/x) }

          α = tan^-1 { mod (0/-3) }

          α = tan^-1 (0)

          α = 0 ...............as tan 0 = 0

• Now by observing the given coordinate (-3,0), we can conclude that it lies in the quadrant II.

• So angle will be:

          Ф = 180 - α

          Ф = 180 - 0

          Ф = 180°

• So the corresponding polar coordinates are (r,Ф) = (3,180°)

Answer:

           So the corresponding polar coordinates are (r,Ф) = (3,180°).