Cannot figure what I am doing wrong: sinx cosx= -1/2

[mrowlet]

Problem: sinc x cos x=-1/2, 0 is less than or equal to x and x < 2 pi


I understand that this is an identity when I multiply 2 by each sides and get sin2x=-12. I also know that in the interval [0,2 pi), there is only one answer for sine=-12 and that is 3pi/4. However, the answer in the book is 3pi/4 and 7pi/4.

When I look at the example in the text, it says that once you get the angle whose angle equals that sine value, to use the double angle of sin 2z=3pi/4. Well, if I do this, I get 3pi/8. This is wher I am LOST! What am I doing wrong? I do NOT want 3pi/8. So, what is wrong? What is the correct next step once I find the angle theta?

 

[Loren]

Problem: sinc x cos x=-1/2, 0 is less than or equal to x and x < 2 pi


I understand that this is an identity when I multiply 2 by each sides and get sin2x=-12. I also know that in the interval [0,2 pi), there is only one answer for sine=-12 and that is 3pi/4. However, the answer in the book is 3pi/4 and 7pi/4.

When I look at the example in the text, it says that once you get the angle whose angle equals that sine value, to use the double angle of sin 2z=3pi/4. Well, if I do this, I get 3pi/8. This is wher I am LOST! What am I doing wrong? I do NOT want 3pi/8. So, what is wrong? What is the correct next step once I find the angle theta?

It would help if you checked for typos before you post. But, not knowing your precise problem, maybe this will help.
You are limited in your answer to 0 < x < 2?.
Therefore 0 < 2x < 4?.
So, you have to consider two revolutions to determine all the possible values of x.

 

[Deleted member 4993]

Problem: sinc x cos x=-1/2, 0 is less than or equal to x and x < 2 pi


I understand that this is an identity when I multiply 2 by each sides and get sin2x=-12.

How is that? You should get

2* sin(x)*cos(x) = 2* (-1/2)

sin(2x) = -1

sin(2x) = sin(3?/2) and sin(7?/2)

Now continue....

I also know that in the interval [0,2 pi), there is only one answer for sine=-12 and that is 3pi/4. However, the answer in the book is 3pi/4 and 7pi/4.

When I look at the example in the text, it says that once you get the angle whose angle equals that sine value, to use the double angle of sin 2z=3pi/4. Well, if I do this, I get 3pi/8. This is wher I am LOST! What am I doing wrong? I do NOT want 3pi/8. So, what is wrong? What is the correct next step once I find the angle theta?