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November 01, 2025, 06:20:28 pm
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Author Topic: How can "r" be negative?  (Read 1620 times)  Share 

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M_BONG

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How can "r" be negative?
« on: July 08, 2013, 03:15:05 pm »
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I'm doing polar coordinates now for GMA and the answer book said "r" is plus or minus a value.

How can this be so? I always thought radius or "r" had to be positive even if it was in the 3rd and 4th quadrant?

Sorry if this is a stupid question I didn't really pay attention in class for this topic.
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Hancock

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Re: How can "r" be negative?
« Reply #1 on: July 08, 2013, 03:15:51 pm »
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"r" should always be positive, as it is a measure of the distance from an origin. The book has a typo I suspect.
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Yeezus

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Re: How can "r" be negative?
« Reply #2 on: July 08, 2013, 03:58:59 pm »
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I recall this problem from high-school, although its counter intuitive, it's not a typo in the textbook.

From memory, you worked it out something like this:

1) Consider the r cis(theta) without the negative.

2) Find the opposite of this ray.

Now, I can't recall how we defined the opposite, but if you do a few examples, you should be able to use this logic to solve that.
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kamil9876

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Re: How can "r" be negative?
« Reply #3 on: July 08, 2013, 04:00:15 pm »
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Perhaps it means in the opposite direction. (For specialist/students who know complex numbers: i.e which is in the opposite direction).

edit: Just saw Yeezus' post:

Quote
Now, I can't recall how we defined the opposite, but if you do a few examples, you should be able to use this logic to solve that.

The opposite of is . If you are familiar with vectors this is like scalar multiplication by . If you are familiar with complex numbers this is multiplication by .
« Last Edit: July 08, 2013, 04:02:00 pm by kamil9876 »
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Yeezus

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Re: How can "r" be negative?
« Reply #4 on: July 08, 2013, 04:38:02 pm »
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Quote from: kamil9876 on July 08, 2013, 04:00:15 pm
Perhaps it means in the opposite direction. (For specialist/students who know complex numbers: i.e which is in the opposite direction).

edit: Just saw Yeezus' post:

The opposite of is . If you are familiar with vectors this is like scalar multiplication by . If you are familiar with complex numbers this is multiplication by .

Yes, I thought this was it, but I wasn't 100% sure, good work.
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