Thread: Trig. Equation.

Well, since I only get an error message telling me that my latex syntax is wrong, I've used this LaTeX engine and pasted the images to this forum.

This is the equation I'm having problems with:


I have rewritten this in terms of sine, like this:




So the equation now looks like this:


I have tried all sorts of things to find the right answer, but I am unable to. This is one of the things I've tried:



But I can't get to the correct answers from this value. Ofcourse I've added +2k pi etc, but I must be doing something wrong. Please help me

Hello,

I don't know your method...
Here's how I'd do :


Let's go back to your equation. You can rewrite it this way :
3sin(2x)+2=4cos(2x)
Square the equation :
9sin²(2x)+12sin(2x)+4=16cos²(2x)

Substituting cos²(2x) by 1-sin²(2x), we have :
9sin²(2x)+12sin(2x)+4=16-16sin²(2x)

25sin²(2x)+12sin(2x)-12=0

Factor this out and find sin(2x)

I am sorry, but this doesn't lead me to the correct answer

This equation is driving me insane, I've been working on it for two days straight... I see that what it left would be basic, but I'd love if you could do the rest of the problem (for all solutions). I'd like to see if you get the same as I do.

In advance, thank you for your time and help :]

(PS: I think LaTeX is working again.)