Question

Find polar coordinates of the point that has rectangular coordinates (-1, -2).

Answer 1

Answer:

Step-by-step explanation:

The length of the polar coordinates ray is found using the Pythagorean Theorem:  ray length = √( (-1)^2 + (-2)^2 ) = √( 1 + 4) = √5

Because both the x- and the y-coordinates here are negative, the ray is in Quadrant III.  Measuring the angle counterclockwise from 0°, we get

Ф = 180° + arctan 2/1, or Ф = 180° + 63.43°, or 243.43°

The desired polar coordinates are (2√2, 243.43°)