Question

Number of soulutions for equation sin2x=sinx (-6,6)?

Answer 1

Hint: Use the identity:

sin 2x = 2(sin x)(cos x)

Answer 2

Another hint:

2(sin x)(cos x) = sin x -> two "branches" of solutions, when:

1) cos x = 1/2 -> (from dividing the above equation by "sin x"

2) sin x = 0

That should lead you to your solution.

Answer 3

How are you doing with this, @zikyo ?

Answer 4

second
DIdnt see you replied :)

Answer 5

Yeah, i got myself to there. But now i dont know how to solve it.

Answer 6

My problem is second part of the equation.

Answer 7

Probably something painfuly obvious ><

Answer 8

cosx=1/2 when x=pi/3

Answer 9

cos x = 1/2 when x = pi/3 OR 5pi/3

I'll send you a graph, hold on.

Answer 10

So, this covers the whole interval.

Answer 11

Yeah, i see it now. Places where two functions meet. There are 7 of them

Answer 12

Yes, that's right. 4 relating to the value for cos x and 3 relating to the sin x.

Answer 13

How would you do it without making a graph?

Answer 14

Is there a way? But i admit, graph is really intuitive way :)

Answer 15

Great question, and yes, you can do this without the graph. And when you can, then you really, really get this super-well because it's close to doing it in your head. First, you concentrate on the positive portion of the interval because when you add on the negative portion, it's just symmetry that will guide you to the negative portion. As for the positive portion:

You have to take into account that x is positive in the first and fourth quadrants. That's key. I usually just start with the reference positions in the first quadrant and subtract that amount. So, in the fourth quadrant I take into account "-pi/3" which is 5pi/3 and see if that is within my interval. Your interval goes up to "6" which is greater than 5pi/3, so you include 5pi/3. But you can't include 2pi (for sin x = 0) because that is greater than 6.

Answer 16

Just what i thouth :D . Tyvm :D

Answer 17

You're very welcome! Hope this all helped! Have a great day! @zikyo

Answer 18

ty :)