# solve a trig problem

• Aug 31st 2011, 02:10 PM
satis
solve a trig problem
Can someone point me in the right direction on how to solve this problem?

$\displaystyle 2sinx - sin2x = \frac{4}{\pi}$

I need to solve for x. I'm honestly not even sure where to begin. I could use double angle identities to turn sin2x into 2sinxcosx, which would then let me turn it into

$\displaystyle 2sinx(1-cosx) = \frac{4}{\pi}$

But I'm not sure how (or if) that would actually help me. Thanks in advance.
• Aug 31st 2011, 02:15 PM
Siron
Re: solve a trig problem
Do you have to solve this exactly?
I gues using a calculator can be very useful, graph the two functions and look at the intersection points.
(Take a look @ wolphram alpha for example, the solution isn't easy)
• Aug 31st 2011, 02:21 PM
satis
Re: solve a trig problem
Oh, ok. Yes, I was trying to solve it exactly. This is actually part of a problem for Calculus 2 (mean value theorem for integrals) that ended up with trying to solve that particular problem to get the two intersection points for f(ave). I was tracking fine with the solution up to that point, but I have no idea where the book pulled the final answer from. I thought it was just my admittedly weak trig skills that were lacking. The book answer did give an approximate answer, so maybe I was just expected to graph it and guesstimate.

I did check out Wolphram (first time user, woo) and the solution look a bit beyond my current math level. Thanks for the post.
• Aug 31st 2011, 02:25 PM
Siron
Re: solve a trig problem
Yes, indeed! The solution is complicated and I don't think it can be solved analytically.