|sinx|=radical3/2

between [-pie;3pie]

how can I radical it?

thanks

You mean:



?

Remember that

Also, is written as pi, not pie.

Now you need to find all the solutions within the range you were given. Do you know how to sketch the y = |sin(x)| graph? This will help you a lot.

hi yes I mean exactly to what u showed
I know how to
sketch the y = |sin(x)| graph is something like this: 0 pi/2 pi 3pi/2...
but I don't sure how to sketch the graph of |sinx|=radical3/2
can u show me ?

thanks for your answer.

Yes, if you know how to sketch it, then do so in the range of -pi to 3pi.

When you equate two equations, like in your example, , we can say that you are solving for the graphs:

and

Now, you sketch the graph of on the same axes.

Can you first tell me how many times the two graphs meet within the domain of -pi to 3pi?

well I know that the Y=radical3 /2 are meet the graph |sin(x)|. 5- times into the domain of -pi to 3pi
but I don't know how many time the graph |sin(x)|=radical3 /2 are meet the graph Y=radical3 /2 into the domain of -pi to 3pi

I need to know the sum of the solutions

THANKS.

Actually, they meet 8 times...

Here's a picture of the two graphs (sorry for the bad quality)

http://p1cture.me/images/49919575412866577834.png

Do you see that the graphs intersect 8 times? One of the solutions, as I told you was at 60 degrees, or at pi/3.

Can you find the other solutions using the picture? Post what you get! :)

YES for sinx|=radical3/2 is need to be like your graph and they have 8 point now I understand it.
but what I don't so understand is how can I find the sum of the solutions?

thank u really much.

Well, you need to find each solution first.

You have the 3rd solution, according to the graph.

The 2nd solution is obviously -pi/3 ()

Then, if you can see the pattern, the solutions are:



Those are the solutions.

If you can notice well, the 'bumps' in this sine curve are symmetrical about the lines and it's odd multiples (that is ). This is where you get the solutions always the same length from the point where the graph touches the x-axis.

Now, you can do whatever you want with them (well, not whatever, but make sure you don't do mistakes.) ;)

Hi the answer is 24pi/3

I really want to thank you about your help.
:)

Yes, correct :)