Question

Which of the following is a solution to 2cos x + 1 = 0? 60° 120° 210° 300°

Answer 1

Answer:

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

Step-by-step explanation:

In this question we have given

$2cos x + 1 = 0$

$2 cos x = -1$

therefore,

$cos x = -\frac{1}{2}$

$x =cos^{-1}( -\frac{1}{2})$

therefore,

$x=120^o$

because cos(120)=$-\frac{1}{2}$

Therefore,

The solution of $2cos x + 1 = 0$ is $x=120^o$

Answer 2

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.