The point with polar coordinates (−2, −135°) could also be expressed as (2, 225°).
Question
The point with polar coordinates (−2, −135°) could also be expressed as (2, 225°).
Solution
Yes, that's correct. In polar coordinates, a negative radius means that the point is in the opposite direction of the angle given. So, a point at (-2, -135°) is the same as the point at (2, -135° + 180°), which simplifies to (2, 45°). However, since we're dealing with degrees, which are cyclical and repeat every 360°, 45° is equivalent to 405°, 765°, -315°, etc. So, 45° and 225° are not the same. Therefore, the point with polar coordinates (−2, -135°) could not also be expressed as (2, 225°). It could be expressed as (2, 45°).
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