|sinx|=radical3/2

between [-pie;3pie]

how can I radical it?

thanks

You mean:

|sin(x)| = \frac{\sqrt3}{2}

?

Remember that sin(60) = \frac{\sqrt3}{2}

Also, \pi 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, |sin(x)| = \frac{\sqrt3}{2}, we can say that you are solving for the graphs:

y = |sin(x)| and y = \frac{\sqrt3}{2}

Now, you sketch the graph of y = \frac{\sqrt3}{2} 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 (-\frac{\pi}{3})

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

-\pi + \frac{\pi}{3} ,\ 0 -\frac{\pi}{3},\ 0 + \frac{\pi}{3},\ \pi - \frac{\pi}{3},\ \pi + \frac{\pi}{3}, \ 2\pi - \frac{\pi}{3},\ 2\pi + \frac{\pi}{3},\ 3\pi - \frac{\pi}{3}

Those are the solutions.

If you can notice well, the 'bumps' in this sine curve are symmetrical about the lines \frac{\pi}{4} and it's odd multiples (that is \frac{3\pi}{4},\ \frac{5\pi}{4},\ etc). 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 :)