Question

What does it mean when the problem asks to find all polar coordinates?

Answer 1

Find all polar coordinates of point p = (6, 31 degrees)

Answer 2

?

Answer 3

but 6sin(31 is -2.4ish

Answer 4

polar coordinates are length (or radius) and angle measured counter-clockwise from the x-axis.
there are an infinite number of angles that will get you to the same point as (6, 31 deg)
i.e. k*360+31 where k is any integer
in other words, if you turn 391 degrees, you end up looking in the same direction as turning 31 degrees.

thus (6, k*360+31) for all integers k
represents many solutions.

also, if we turn 180+31 degrees and then move -6 (think "walk backwards")
we also end up at the same point.

thus <-6, 211 deg> is another way to get to <6,31>
and just like the first case, we can add any multiply of 360 degrees:
< -6, 211+ k*360> , k any integer

is the other "family" of ways to specify the same point

Answer 5

Ok