SOLUTION: √3*sin(x/2)+cos(x/2)=0 (π≤x<4π)

Question 1029560: √3*sin(x/2)+cos(x/2)=0
(π≤x<4π)
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.
√3*sin(x/2)+cos(x/2)=0
(π≤x<4π)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 =   --->  (divide bith sides by 2)  ---> 

 = .   (1)

Notice that  =   and   = .

Therefore, you can rewrite (1) as

 = .   (2)

Now apply the addition formula for sine  = .

You will get instead of (2)

 = .

Then  pi/6 + x/2 = ,  k = 0, +/-1, +/-2, . . . 

Hence x = .

To get the given interval for x, take k = 1 and k = 2.

You will have two solutions  x =  =   and  x =  = .

Answer. There are two solutions in the given interval. 

        They are  x =   and x = .

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SOLUTION: √3*sin(x/2)+cos(x/2)=0 (π≤x<4π)