MHB Eaglesfan1717's question at Yahoo Answers regarding a trigonometric equation

[MarkFL]

Here is the question:

Help with trig equation :)?

sin x = 2 sin x cos x

Here is a link to the question:

Help with trig equation :)? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Hello eaglesfan1717,

We are given to solve:

$$\sin(x)=2\sin(x)\cos(x)$$

I would arrange the equation so that we may factor and utilize the zero-factor property:

$$2\sin(x)\cos(x)-\sin(x)=0$$

$$\sin(x)(2\cos(x)-1)=0$$

Equating the factors in turn to zero yields the following roots:

i) $$\sin(x)=0$$

$$x=k\pi$$ where $$k\in\mathbb{Z}$$.

ii) $$2\cos(x)-1=0$$

$$\cos(x)=\frac{1}{2}$$

$$x=\pm\frac{\pi}{3}+2k\pi=\frac{\pi}{3}(6k\pm1)$$

To eaglesfan1717 and any other guests viewing this topic, I invite and encourage you to post your trigonometry questions in our http://www.mathhelpboards.com/f12/ forum.

Best Regards,

Mark.