Jambo is not the son of Oscar

[logistic_guy]

Polar coordinates. Given a point \(\displaystyle P\) in the \(\displaystyle xy\)-plane, a pair of numbers \(\displaystyle (r; \theta)\) can be assigned, in which \(\displaystyle r\) is the distance from \(\displaystyle P\) to the origin \(\displaystyle O\), and \(\displaystyle \theta\) is the size of an angle in standard position that has \(\displaystyle OP\) as its terminal ray. Notice that there is more than one correct value for \(\displaystyle \theta\). Find polar coordinates for the following pairs \(\displaystyle (x; y)\), giving at least two values of \(\displaystyle \theta\) for each:

\(\displaystyle \bold{(a)} \ (0; 2)\)
\(\displaystyle \bold{(b)} \ (-1; 1)\)
\(\displaystyle \bold{(c)} \ (8;-6)\)
\(\displaystyle \bold{(d)} \ (1; 7)\)
\(\displaystyle \bold{(e)} \ (-1;-7)\)

 

[jonah2.0]

Beer drenched non sequitur ramblings follow.

Polar ...

Eating nothing but rice for a two days will make your mind wonder if aliens are walking amongst us. Eating nothing but rice for two more extra days will make you wonder why aliens would want to spend time on earth at all. Are they here for our gold?

 

[khansaheb]

. Are they here for our gold?

No.....

Men from Mars are eating our cars (Blondie)

 

[The Highlander]

Polar coordinates. Given a point \(\displaystyle P\) in the \(\displaystyle xy\)-plane, a pair of numbers \(\displaystyle (r; \theta)\) can be assigned, in which \(\displaystyle r\) is the distance from \(\displaystyle P\) to the origin \(\displaystyle O\), and \(\displaystyle \theta\) is the size of an angle in standard position that has \(\displaystyle OP\) as its terminal ray. Notice that there is more than one correct value for \(\displaystyle \theta\). Find polar coordinates for the following pairs \(\displaystyle (x; y)\), giving at least two values of \(\displaystyle \theta\) for each:

\(\displaystyle \bold{(a)} \ (0; 2)\)
\(\displaystyle \bold{(b)} \ (-1; 1)\)
\(\displaystyle \bold{(c)} \ (8;-6)\)
\(\displaystyle \bold{(d)} \ (1; 7)\)
\(\displaystyle \bold{(e)} \ (-1;-7)\)

 

[The Highlander]

Correction to previous post:-

Where it says:-

"unless you choose also to measure it anti-clockwise from zero"​

it should, of course, have read:-

"unless you choose also to measure it clockwise from zero"​

(Just a wee slip of the pen. )

 

[Dr.Peterson]

You've seen the wrong sources! Of course that formula is wrong, even more than you say here! The usual formula uses atan2:

Polar coordinate system - Wikipedia

en.wikipedia.org

​

That accounts for the quadrant.

Polar coordinates can be defined uniquely, but the author chose not to. That is not uncommon:

Polar coordinate system - Wikipedia

en.wikipedia.org

​

You may not recognize this, but in answering a question, the standard policy is to accept the givens. Here is the source :

https://exeter.edu/app/uploads/2024/08/Math4_2024_printed.pdf

(This, by the way, doesn't use the semicolon, but that is in fact standard in countries where comma is used as the decimal separator.)

Of course, I say all this in contravention of my policy of ignoring threads that are started under false pretenses. I'll go back into my silence now.