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Factoring with Trigonometry

Date: 3/5/96 at 20:38:26
From: Anonymous
Subject: A question about trig.


Please will you help me out in math on this one problem.

    4tan^2X + 7tanX - 2 = 0


Date: 3/6/96 at 13:0:11
From: Doctor Elise
Subject: Re: A question about trig.


Okay, don't panic because you have tanX in there.  Let's 
substitute Y = tanX for now, and plug the tanX back in later.  
Then your problem becomes:

4Y^2 + 7Y - 2 = 0

If we factor this, we get

(4Y - 1)(Y + 2) = 0, right?  

Solving for Y, we know that one or the other term = 0, so 

(4Y - 1) = 0  or  (Y + 2) = 0

  Y = 1/4     or    Y = -2

Now we can put back the Y = tanX, and we have

tanX = 1/4    or   tanX = -2

And now you need a tangent table to find the actual
values for X that work.

Does this help?

-Doctor Elise,  The Math Forum

Associated Topics:
High School Trigonometry

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