Polar coordinates: find other coords for (-3, -pi/4)

[Violagirl]

Hi, I'm not sure how I am doing this problem wrong and if someone could show me what is that I am doing wrong, that would be great!

Plot the point given in the polar coordinate, and find other polar coordinates (r, theta) of the point for which:

a. r>0, -2pi<theta<0, b. r<0, 0<theta<2pi, c. r>0, 2pi<4pi

(-3, -pi/4)


I know that for the first one you are supposed subract 2pi, for the second one replace with -r and add pi, and for the third add 2pi. I'm having a hard time finding the right answers.

For the a. I got -3, -7pi/4, for b. got 3, 3pi/4, and for c found -3, 9pi/4. The answers in my book got for a. (3, -5pi/4, b. -3, 7pi/4, and for c. (3, 11pi/4). Any help would be great!

 

[Aladdin]

Re: Polar coordinates

Hi, I'm not sure how I am doing this problem wrong and if someone could show me what is that I am doing wrong, that would be great!

Plot the point given in the polar coordinate, and find other polar coordinates (r, theta) of the point for which:

a. r>0, -2pi<theta<0, b. r<0, 0<theta<2pi, c. r>0, 2pi<4pi

(-3, -pi/4)

a.For r>0 we can see that when rotating theta -180 degrees we attain (3 ,-5pi/4)According to the Interval
b.for r<0the same point is attained when rotating theta 360 degrees-3.7pi/4)
c.for r>0 and theta between2pi and 4pi add 3pi(3,11pi/4)

 

[soroban]

Re: Polar coordinates

Hello, Violagirl!

The book's answers are correct.

Plot the point given in the polar coordinate: .\(\displaystyle \left(\text{-}3,\:\text{-}\tfrac{\pi}{4}\right)\) . The point is in Quadrant 2.

                |
        o       |
          *     |
            *   |
              * |
      - - - - - * - - - - -
                |

and find other polar coordinates \(\displaystyle (r,\:\theta)\) of the point for which:

. . \(\displaystyle (a)\; r>0,\;-2\pi \leq \theta \leq 0\qquad (b)\; r<0,\;0 \leq \theta \leq 2\pi\qquad (c)\;r>0,\;2\pi\leq \theta \leq 4\pi\)

For (a) I got: \(\displaystyle \left( \text{-}3,\:\text{-}\tfrac{7\pi}{4}\right)\) . . . . no

Your angle is in Quadrant 1.
Besides, they asked for a positive \(\displaystyle r.\)

For (b) I got: \(\displaystyle \left(3,\:\tfrac{3\pi}{4}\right)\) . . . . no

They asked for a negative \(\displaystyle r.\)

For (c) I got: \(\displaystyle \left(\text{-}3,\:\tfrac{9\pi}{4}\right)\) . . . . no

They asked for a positive \(\displaystyle r.\)
Besides, \(\displaystyle \tfrac{9\pi}{4}\) is in Quadrant 1.