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 Geometry and Trigonometry
 different values of cosine
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ep6
Junior Member

USA
4 Posts

Posted - 10/05/2007 :  12:58:01  Show Profile
I am having a little problem. =90. So that means that to make a complete circle it is 2. If i have 13/4. That means it makes 3 revolutions and then /4=45 degrees. That means that
cos13/4 = (-2). Now if we pick the value 9/4 and try to find the cosine of that, shouldn't it be the same value as 13/4? When I put it in the calculator, it tells me that cos9/4 is equal to 2/2. Can anyone explain to me how its positive and not negative?
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skeeter
Advanced Member

USA
5634 Posts

Posted - 10/05/2007 :  13:19:41  Show Profile
first off, does not equal 90 ... radians is equivalent to 180 degrees of arc. 2 radians is equivalent to 360 degrees of arc.

13/4 - 2 = 5/4 ... this says that 13/4 and 5/4 are coterminal. 5/4 resides in quadrant III, so ...

cos(13/4) = cos(5/4) = -(2)/2

also ... 9/4 - 2 = /4, which resides in quadrant I ... its cosine is (2)/2.
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ep6
Junior Member

USA
4 Posts

Posted - 10/05/2007 :  13:21:49  Show Profile
i see. thanks a lot for the clear up. now i understand

Edited by - ep6 on 10/05/2007 13:23:14
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 10/05/2007 :  13:24:59  Show Profile
You seem to have the right basic idea for the circular definition of the cosine, but you don't seem to be using your calculator correctly.

First off, If your calculator said the cosine of anything is 2, positive or negative, something is seriously wrong. Perhaps you just forgot to type in the "/2" when you said that.

Second, the INVERSE cosine is a very different animal. It is NOT defined for the entire Range of the Cosine function. The INVERSE cosine function will supply values only between 0 and . It is your responsibility to deal with anything not in that region.

Third, even though you stated it correctly at first, you forgot to go 2. 13/4 - 9/4 = . You moved from Quadrant III to Quadrant I. The sign had better change from negative to positive when you do that. If you had moved 8/4 = 2, all the way to 5/4, then it would be reasonable to expect the same answer as 13/4.
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