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### Factoring with Trigonometry

```
Date: 3/5/96 at 20:38:26
From: Anonymous

Hello,

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

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

Thanks
```

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

Hi!

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

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
either

(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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