# converting rectangular coordinates to polar

• May 25th 2009, 09:03 PM
tomatoes
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
• May 25th 2009, 11:09 PM
Polar coordinates
Hello tomatoes
Quote:

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 $0^o$ and $360^o$, then you'll need to subtract $53$ from $360$, which is where the $307$ comes from.

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