SOLUTION: sin(2x) = -sqrt(2)/2 have to find what points on the unit circle would equal that

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Question 1102259: sin(2x) = -sqrt(2)/2
have to find what points on the unit circle would equal that
Found 2 solutions by Lightning_Fast, ikleyn:
Answer by Lightning_Fast(78)   (Show Source): You can put this solution on YOUR website!
Well the 2x there is a little crazy, so replace 2x with z. In other words, z = 2x.
Now the equation is:

Now from the unit circle, we know that z must be equal to 125 and 315 degrees. Now you know what z is in degrees, you can use the previous equation.
z = 2x
Now you obtain the following.
125 = 2x
315 = 2x
Now use algebra and solve for x. But remember the x value is NOT the point on the unit circle that will equal -sqrt(2)/2. It is just a solution to the equation.


If you want to find the points on the unit circle that satisfy this equation, you just have to look at the unit circle.
The values appear to be , ) and (, )
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
The solution by @Lightning_Fast is partly WRONG and partly INCOMPLETE, so NEITHER PART OF HIS SOLUTION IS USEFUL.

Below please find the CORRECT solution. 

sin(2x) =   ======================>


This equation has two solutions for 2x:


1)  2x =    or   2)  2x = .


Case 1.  2x =   has TWO solutions for the angle x:  

                                                   a)  x =   and

                                                   b)  x =  = .



Case 2.  2x =   has TWO solutions for the angle x:  

                                                   a)  x =   and

                                                   b)  x =  = .


Answer.  The given equation has four solutions:  ,  ,    and  .

Solved.


The plot below CONFIRMS existing of four solutions in the interval [0, ):




Plot y = sin(2x) (red) and y = (green)


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