Trig problem

Kadith

Okay, I've pretty much exhausted everything I know about trig trying to figure this one out, I'm sure it's probably something simple I'm forgetting, but here it is

cos^2(x) - sin^2(x)=sin (x)

where is x is between pi and negative pi.

So if someone could point me in the right direction of steps that would be great.

Thanatos

Isn't there a trig identity for cot^2(x)-1?

Abels

Replace cos^2(x) with something like 2sin^2(x/2) (I can't remember it exactly, but there's a great wikipedia page on trig identities. If you're looking for some fun, memorize euler's equation to derive all the real and complex trig identities you can handle!)

Hirocon

Replace cos^2(x) with (1 - sin^2(x)), then solve a quadratic equation for sin(x). There are two solutions for sin(x), and two solutions for x between negative pi and pi.

BlochWave

Replace cos^2(x) with something like 2sin^2(x/2) (I can't remember it exactly, but there's a great wikipedia page on trig identities. If you're looking for some fun, memorize euler's equation to derive all the real and complex trig identities you can handle!)

oh heavens no, trying to use a half-angle formula would drive you into the mud

Do what the previous poster recommended.

For so very many many many situations, sin^2+cos^2=1 (variable omitted for clarity of typing)will get you so very far. Just remember that tan is sin/cos and cot is cos/sin(the COtan has the COsin on top)People tend to overcomplicate these in ways that makes them impossible, quoted poster is case in point

By the time he's learning e^(ix)=cos(x)+i(sinx) he'd probably be in classes that'd allow a calc that could sort out trig functions

Abels

BlochWave wrote: »

classes that'd allow a calc that could sort out trig functions

HA

BlochWave

Why the ha?

I learned euler's identity in a math method for physicists class, which was after all my calculus and a normal ODE course, so by then I had a TI-89 and was allowed to use it

I don't recall needing to know many of the exotic trig functions for LA or PDE classes anyways(maybe some of the angle sum ones, cos(a+b)=? types)

Kadith

Thanks, a lot guys. I've never had to combine the quadratic and trig before so I never tried working that out.

Although there were actually three solutions but I could use one to find the last one.

Big Dookie

BlochWave wrote: »

I learned euler's identity in a math method for physicists class, which was after all my calculus and a normal ODE course, so by then I had a TI-89 and was allowed to use it

Yeah, I'd heard of it before, but I never truly learned it until I had to use it for phasors in my Circuits class. Since then though I've used it in almost every class I've had at one point or another.

In any case, yeah, the best course of action in many of these problems is to simply memorize the cos squared plus sin squared equals one equation, and derive whatever else you need from that. I'm terrible at remembering trig identities for the most part, but I can almost figure out what I need to be just remembering that one formula.