Math Is Fun Forum

Newman

Member

Registered: 2015-09-21

Posts: 42

Factoring Tangent

Can this be factored or do you have to do quadratic formula?? Does the fact that it's an angle give it any unique workable properties or do I just look at coefficients like any other quadratic? Thanks.

1tan^2x + 3tanx -1 = 0

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring Tangent

Hi;

If you mean this:

then just make the substitution y = tan(x) and solve like any other polynomial.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring Tangent

Yes, that's what I meant. Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring Tangent

Did you solve the equation?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring Tangent

Yup.

I just did x = b+/- blah blah to get tanx=.303 and -3.303.

So, tan^-1's =

16.86 degrees (.29 rad) and 196.86 degrees (pi+.29 rad).
And
286.84 degrees (1.28 + 2pi rad) and 106.84 degrees (pi - 1.28 rad).

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring Tangent

While concept was forming in my head, I was wondering if functions could change (x + y)(x + y) (factoring) vs quadratic approaches so that factoring might work where it doesn't without tangents, cosines etc...However, I realized that doesn't really make sense so that quadratic equation was necessary.

That was sort of the rationale behind my original question. I realize it's sorta nonsense tho. Factoring clearly wasn't going to work. Unless I'm missing something else...which, of course, is very possible. Lol

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring Tangent

You can always factor a quadratic, but not always simply.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.