Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

Question

anonymous · Answer

Substitute sin 2x. Here's your cheat sheet http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

anonymous · Answer

Can you show me the full solution please?

anonymous · Answer

Try my suggestion, I would correct you if you do something wrong.

anonymous · Answer

sin(2x)=2sin(x)cos(x)
then you get 
2cos(x)+2cos(x)sin(x)=0

2cos(x)(1+sin(x))=0

cos(x)=0
 or 
1+sin(x)=0

sin(x)=−12

anonymous · Answer

-1/2*

anonymous · Answer

The two different quantities in brackets are multiplied; or rather the three quantities are multiplied, so when evaluating each the other two go to zero. The 2 can actually be ignored.
So cos(x)=0
1 + sin x=0
sin x= -1

anonymous · Answer

in that interval cosine  is 0 at 
π2
 and 
3π2

anonymous · Answer

sin(x)=−1/2
and see that it is at 
7π/6
 and 
11π/6

anonymous · Answer

$$x =\cos^{-1} 0$$$$x =\pi/2,(3\pi/2)$$$$x =\sin^{-1} -1$$$$x =(3\pi/2)$$(Remember there is no -1/2. The 2 goes to 0.