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Thread: converting rectangular coordinates to polar

  1. #1
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    converting rectangular coordinates to polar

    rectangular coordinates: (6, -8)

    ok i got r=10 which im pretty sure is right but im unsure about q.

    q=tan-1(y/x)
    so i got q= -53.13)

    but i checked it on a conversion thing and it said q is like 307??? what did i do wrong
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  2. #2
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    Polar coordinates

    Hello tomatoes
    Quote Originally Posted by tomatoes View Post
    rectangular coordinates: (6, -8)

    ok i got r=10 which im pretty sure is right but im unsure about q.

    q=tan-1(y/x)
    so i got q= -53.13)

    but i checked it on a conversion thing and it said q is like 307??? what did i do wrong
    Your answer is OK, but if you need to give an angle between $\displaystyle 0^o$ and $\displaystyle 360^o$, then you'll need to subtract $\displaystyle 53$ from $\displaystyle 360$, which is where the $\displaystyle 307$ comes from.

    There are two values of $\displaystyle \theta$ in the range $\displaystyle 0\le\theta<360$ for which $\displaystyle \tan\theta = -\tfrac43$. They are (to the nearest degree) $\displaystyle 180 - 53 = 127^o$ and $\displaystyle 360 - 53 = 307^o$. Since $\displaystyle (6, -8)$ is in the fourth quadrant, the answer you want is $\displaystyle 307^o$.

    Grandad
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