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coterminal angle

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hi,

 

I am having a little problem with conterminal angles. I know what they are as defined by my textbook as "...sum of there degree measure is 360 or a multiple of 360".

 

But I am not certain about the "multipe of 360" part. According to what I've read, the rotation has to be multiple of 360. And that's pretty striaght-forward. But in the book following example contradicts the statement, as far as I am concerend:

 

870 - 360 = 510

510 - 360 = 150

 

It's stated that 870 and 150 are coterminal angles. But 870+150 =1020 / 3 =340; not 360.

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Err... No, coterminal angles are not that. They are angles which share the same arm when put in standard position. So imagine a Cartesian plane and an arm extending a certain angle from the x axis, rotating counterclockwise. That's an angle in standard position. So, say you have an angle at 30 degrees at standard position.

 

Its coterminal angles would include 390, because you have a 360 rotation about the origin more then add the 30 degrees upon that 360.

 

In that sense, 750 degrees is a coterminal angle of 30 as well, but with two rotations (720 degrees more), and so are 1110 (3 rotations), 1470 (4) and so on.

 

So, this way, 870 and 150 are coterminal angles. Why? Well, 870 when put in standard position is definitely more than 2 full rotations because it is larger than 720 degrees. So subtracting the 2 rotations from the angle gives an angle with the same arm, or a coterminal angle. 870-720=150, thus 870 and 150 are coterminal angles.

 

Also, negative angles can be coterminal angles of positive angles too, and vice versa. A negative angle in standard position is starting from the x axis, just like a positive angle, but instead of rotating counterclockwise, it goes clockwise. So, a 30 degree angle in standard position is coterminal with a -330 degree angle.

 

So, I think your textbook's wrong.

 

EDIT: I've drawn a picture for you (yes yes, you can marvel at my artistic sk1llZ - one of the many talents I was born with :D jk). The 45 denotes, well, the 45 angle in standard position. The 405 is coterminal with the 45 degree angle, because it goes from the x axis all around 360 degrees, then end up at THE SAME ARM.

SAngle.JPG

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The Thing - That's what I was suspecting but stupid review book was turning my off. Whatsoever, this mistake in the book has made realize again that everything I read in my textbooks are not to be treated as the "divine texts" revealed by God. Anybody, anywhere can prove them wrong using the power of knowledge.

 

JustStuit - That means you're moving the ARM (or the terminal side) back to the origin. In other words, you're subtracting an incomplete third rotation to have the complete two rotations.

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The Thing - That's what I was suspecting but stupid review book was turning my off. Whatsoever' date=' this mistake in the book has made realize again that everything I read in my textbooks are not to be treated as the "divine texts" revealed by God. Anybody, anywhere can prove them wrong using the power of knowledge.

 

JustStuit - That means you're moving the ARM (or the terminal side) back to the origin. In other words, you're subtracting an incomplete third rotation to have the complete two rotations.[/quote']

Ah I see. Maybe the book subtracted instead of adding by accident. Seems pretty careless of them - and to not double check too.

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