# Thread: converting rectangular coordinates to polar

1. ## 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

2. ## Polar coordinates

Hello tomatoes
Originally Posted by tomatoes
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 $\displaystyle 307^o$.