arccot( cot( -7 ))
ti-89 says 3*pi - 7
But how. I cannot find any good geometric interpretation.
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.
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.
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.