You have just two cases:
Find the value of x of the following trigonometric equation with x is between -pi and pi
| sin 2x | = 1/2
sin 2x = 1/2 (case 1)
2x= 30 , 150
x= 15 and 75
sin (-2x) = 1/2
There is no solution for this .
sin 2x = -1/2
sin (-2x) = -1/2
-2x = 30 , 150
x = -15 , -75
Am i correct ??
As red_dog has said, you need to solve two equations
Since you want values of between and , you'll need to look at values of between and .
I always find the graph of easier to use than the unit circle, so look at the sketch I've attached. The easiest value is, of course, . Look at where the dotted lines intersect the graph. They are at:
So these are the possible values of . Divide them all by , and you're done.
You'll see that I've drawn a rectangle around the section of the graph between and - rectangle number (1). This rectangle is then rotated about the point to form rectangle (2). And it has been translated through to form rectangle (3) ... And so on, to create as many sections of the graph as you need.
Now we know that the first value where is . Using this graph you can see that there are others where and , , ... So the solutions between are .
We can also work out in the same way where . Rectangle (2) shows that there will be one value at . And there'll be others at etc.
Provided you can sketch the graphs of sine, cosine and tangent quickly - and it's worth learning them - I think you'll find this is a great help in solving trig equations.