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what is the acute angle of tan A=u/v?

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maii-maii | Student, College Freshman | eNotes Newbie

Posted November 24, 2011 at 10:03 PM via web

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what is the acute angle of tan A=u/v?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 25, 2011 at 11:08 PM (Answer #1)

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An acute angle is smaller than 90 degrees, therefore the acute angle A belongs to the interval `(0^o,90^o)` .

The acute angle A is: A = `tan^-1(u/v)` = `arctan (u/v)`

If `A=30^o =gt tan 30^o =(u/v) = (sqrt3)/3`

If `A=45^o =gt tan 45^o =(u/v) = 1`

If `A=60^o =gt tan 60^o =(u/v) = sqrt 3`

Notice that the value of the quotient `u/v`  increases, if the acute angle increases.

ANSWER: A = `arctan (u/v) = tan^-1(u/v)`

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