Respuesta :

altavistard
Rewrite   2cos x + 1 = 0    as:

2 cos x = -1, and then cos x = -1/2

x must be in Quadrant II or Quadrant III, since the adj. side is negative.

Note that the angle 120 has adj. side -1 and hyp 2.  So 120 degrees is one solution.  

Now what about a possible 2nd solution, to be found in Quadrant III?  That would be -120 degrees, which has the same terminal line as does 240 degrees.

No soap.

So, the solution is 120 degrees.

Answer:

correct answer is second option (The solution of [tex]2cos x + 1 = 0[/tex] is [tex]x=120^o[/tex])

Step-by-step explanation:

In this question we have given

[tex]2cos x + 1 = 0[/tex]

[tex]2 cos x = -1[/tex]

therefore,

[tex]cos x = -\frac{1}{2}[/tex]

[tex]x =cos^{-1}( -\frac{1}{2})[/tex]

therefore,

[tex]x=120^o[/tex]

because cos(120)=[tex]-\frac{1}{2}[/tex]

Therefore,

The solution of [tex]2cos x + 1 = 0[/tex] is [tex]x=120^o[/tex]

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