## anonymous 5 years ago Find all the values of x in the interval [0, 2pie] that satisfy the equation 2cos(x) + sin(2x) = 0.

1. anonymous

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

2. anonymous

Can you show me the full solution please?

3. anonymous

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

4. anonymous

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

5. anonymous

-1/2*

6. anonymous

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

7. anonymous

in that interval cosine is 0 at π2 and 3π2

8. anonymous

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

9. anonymous

$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.