You have just two cases:
and
Find the value of x of the following trigonometric equation with x is between -pi and pi
| sin 2x | = 1/2
My work
sin 2x = 1/2 (case 1)
2x= 30 , 150
x= 15 and 75
sin (-2x) = 1/2
There is no solution for this .
case 2
sin 2x = -1/2
no solution
sin (-2x) = -1/2
-2x = 30 , 150
x = -15 , -75
Am i correct ??
Hello thereddevils
As red_dog has said, you need to solve two equations
and
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.
Grandad
Hello thereddevilsAbsolutely! Just sketch the graph, then use the section between and (the bit I've indicated below inside the red rectangle) as a 'building block', rotating and reflecting it as necessary, to create the whole graph, for any range of values you want. Then, provided you know the angle in the range to , you can easily work out the corresponding angle in any other range.
Grandad
Hello thereddevilsHave a look at the diagram I've attached, which shows a sketch-graph of , between , and the line as a dotted line.
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.
Grandad