# Thread: Find x in trig equation

1. ## Find x in trig equation

Hi there,

"Solve 6sin2x + sinx - 2 for all x in 0 < x < pi/2"

I know through graphing that the answer is pi/6. Is there another way of proving this?

thanks

2. ## Re: Find x in trig equation

You may also treat it as a quadratic equation and then the values can be found. For ax^2 + bx + c = 0; we have x = [ -1 +/- sqrt ( b^2- 4ac )]/ 2a
In this case you will get sin x = [ -1 +/- sqrt ( 1+ 48 )]/ 12
now solve it further

3. ## Re: Find x in trig equation

So I get sin x = 1/2 and -2/3.

How do I then solve x for x in 0 < x < pi/2? Is it simply 1/2?

4. ## Re: Find x in trig equation

Sin pi/6 = 1/2 and sine is positive in first and second quadrant. Thus we have sin pi/ 6 = sin ( 5pi/6 ) = 1/2
i hope it is ok now similarly for the other value. remember sine is negative in third and fourth quadrant.