Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I know I'm supposed to do $\sin(3x) - \sin x = 0$ but beyond that I'm stuck.. I tried expanding $\sin(3x)$ but that didn't help.

  • I want the value of $x$ in the interval $[0, 2\pi)$
share|improve this question
2  
This is homework I suppose. Please tag it as such. –  Aryabhata Sep 30 '10 at 18:58
    
@Moron not really but if it pleases you .. –  andrei Sep 30 '10 at 19:09

2 Answers 2

up vote 6 down vote accepted

We have $\sin{3x} = 3\sin{x} - 4\sin^{3}{x}$ which says that we have to solve the equation $$3\sin{x} - 4\sin^{3}{x} - \sin{x}=0$$, that is $2 \sin{x} - 4\sin^{3}{x}=0$. Take $y = \sin{x}$ and so you have $$2y-4y^{3}=0 \Longrightarrow 2y(1-2y^{2})=0$$ and then see what happens. I hope this helps you out.

Or you can even try this $$\sin{3x} - \sin{x} = 2 \cos\Bigl(\frac{3x+x}{2}\Bigr) \cdot \sin\Bigl(\frac{3x-x}{2}\Bigr) = 2\cos{2x} \cdot \sin{x}$$

share|improve this answer
    
ow silly me i thought sin3x = 3sinx - 4cos^3(x) –  andrei Sep 30 '10 at 19:08
    
Can i divide by y ? and get 2 - 4y^2 ? –  andrei Sep 30 '10 at 19:10
    
@Andrei: You should think on your own, from now! –  anonymous Sep 30 '10 at 19:26
    
Yes thank you! i try to think on my on from now sorry >.< –  andrei Sep 30 '10 at 20:06
2  
@andrei: regarding dividing by y, consider whether there any numbers that you cannot divide by. –  Isaac Sep 30 '10 at 20:27

You could use the fact that $\sin x=\sin y$ if and only if either $x-y$ is an even integer times $\pi$ or $x+y$ is an odd integer times $\pi$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.