Positive angle and negative angle. Explain please.

Indranil

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Feb 22, 2018
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215
My book says,
''consider a ray OA. If this ray revolves about its end point O in an anti-clockwise direction and takes position OB, then we say the angle ∠AOB has been generated as a positive angle and a negative angle. or simply say that angle is a measure or an amount of revolution of a given ray about its initial point.
The angle is positive or negative if the initial line revolves in anti-clockwise or clockwise direction to get the terminal line''

Still, I cannot understand the concept. Could you get the point easier for me, please?
 

Dr.Peterson

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Nov 12, 2017
Messages
3,101
My book says,
''consider a ray OA. If this ray revolves about its end point O in an anti-clockwise direction and takes position OB, then we say the angle ∠AOB has been generated as a positive angle and a negative angle. or simply say that angle is a measure or an amount of revolution of a given ray about its initial point.
The angle is positive or negative if the initial line revolves in anti-clockwise or clockwise direction to get the terminal line''

Still, I cannot understand the concept. Could you get the point easier for me, please?
The wording is a little odd; did you quote it word for word?

The basic idea is that anti-clockwise (or counter-clockwise) rotation is considered to be positive, and clockwise rotation is negative.

I would restate your sentence, "The angle is positive or negative if the initial line revolves in anti-clockwise or clockwise direction to get the terminal line" as "The angle is positive if the initial line revolves in an anti-clockwise direction to the terminal line, and negative if the initial line revolves in a clockwise direction".

So if we start with OA and rotate 90 degrees clockwise to OB, we say that AOB is -90°.
 

Indranil

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Feb 22, 2018
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215
1. Could you provide a figure in support of it?
2. Could you discuss 'initial line' and 'terminal line' so I can understand well, please?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,101
1. Could you provide a figure in support of it?
2. Could you discuss 'initial line' and 'terminal line' so I can understand well, please?
Does your book not have a picture? That is difficult to believe.

What part do you not understand? Are you saying you don't know what "initial" and "terminal" mean? Please be specific; I can't help you understand without knowing where you need help.

Let's look for a picture and explanation online. Here are two I found by searching for "signed angles initial terminal": Oxford Math Center; Math Open Reference. There are many more.

Where you used the word "line", these use "side".
 

Indranil

Junior Member
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Feb 22, 2018
Messages
215
I understand now. Thank you for your kind effort. Thanks a lot.
 
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