Trig functions: looking for a good way to find exact value of
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Trig functions: looking for a good way to find exact value of

[From: ] [author: ] [Date: 11-04-30] [Hit: ]
Well, arccot(cot(x)) = x except that x is reduced to be in the principal range of the arccot:0 to pi.So, arccot always returns an angle in the first or second quadrant.Since -7 was in the fourth quadrant it got adjusted to an equivalent reference angle in the second quadrant.It could have been pi - 7,......
arccot( cot( -7 ))

ti-89 says 3*pi - 7

But how. I cannot find any good geometric interpretation.

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Remember, because all the trig functions are periodic the arc functions must be restricted to return values in a principal range. Otherwise the arc functions wouldn't be functions, they would have to return multiple values.


Well, arccot(cot(x)) = x except that x is reduced to be in the principal range of the arccot: 0 to pi.
So, arccot always returns an angle in the first or second quadrant.

Since -7 was in the fourth quadrant it got adjusted to an equivalent reference angle in the second quadrant. It could have been pi - 7, too. I don't know why it chose 3pi-7 instead of pi -7, perhaps there is some setup which can be adjusted.

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Obviously arccot(cot(x)) = x.
More generally though arccot(cot(x)) = 2pi(n) + x where n is an integer.
your calculator just gave 3pi-7 since that value is the one between 0 and 2pi.
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