# Math Help - Trigonometric equation

1. ## Trigonometric equation

Hello,

I have made attempts to find the solutions to th eeqution 2 sin x + csc x = 0 on the interval [0, 2pi). So, in my disconcertion, I flipped to the answer key and found the steps to finding solution. The steps are as follows:

2 sin x + csc X = 0 ---> 2 sin x + 1/sin x = 0

2 sin x + 1 = 0

What did they do to procure step three? Where did the denominator go? On that step I had gotten (2 sin x + 1)/sin x.

Thank you

2. ## Re: Trigonometric equation

Your intermediate step is fine. But the only way a fraction can be equal to 0 is if the numerator is 0.

3. ## Re: Trigonometric equation

I disagree w/ the "answer" key ...

$2\sin{x} + \frac{1}{\sin{x}} = 0$

$\frac{2\sin^2{x} + 1}{\sin{x}} = 0$

this equation has no real solution.

4. ## Re: Trigonometric equation

Whoops, I should have spent more time checking.