Expert: Sherman D. - 3/11/2008

Question
Hi,
As part of a more complex dynamics problem I have used equations of motion and trigonometric identities to come down to a final equation but I am now stuck. The equation is:

9.734=19tanTHETA+9.034tan^2THETA

I am trying to solve for THETA but am having trouble because one of the tans is squared.
Any help would be most appreciated.

Answer
9.734 = 19tan(A) + 9.034tan(A)^2

this is actually quite simple

9.034tan(A)^2 + 19tan(A) - 9.734 = 0

The Quadratic Formula
tan(A) = (-19 ± sqrt(19^2 - 4(9.034)(-9.734)))/(2(9.034))
tan(A) = (-19 ± sqrt(361 + 351.747824))/18.068
tan(A) = (-19 ± sqrt(712.747824))/18.068

A = about 23.075° or 203.075°, about 291.573 or 111.573

the reason for the four answers, is because the first 2 answers are for

tan(A) = (-19 + sqrt(712.747824))/18.068

and the second 2 are for

tan(A) = (-19 - sqrt(712.747824))/18.068