Question

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

Answer 1

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

Explanation:

In this question we have given

`2cos x + 1 = 0`

`2 cos x = -1`

therefore,

`cos x = -(1)/(2)`

`x =cos^(-1)( -(1)/(2))`

therefore,

`x=120^o`

because cos(120)=
`-(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.