Solve 2 cos x + 1 = 0, when 0≤ x ≤ 360˚?

Question

When 0≤ x ≤ 360˚, solve 2 cos x + 1 = 0

Answer 1

Subtract 1 from both sides:
2 cos x=-1

Divide 2 from both sides:
cos x=-1/2
x=2π/3,4π/3
x=120°,240°

Answer 2

Ok, you can solve this for x and find that x as a reference angle is 60 degrees. But how to get the negative in there...
you need a reference angle of 60 degrees, and you need to remember that cosine follows the x coordinate on the unit circle. The x coordinate is negative in the second and third quadrants so you need your 60 degree refernce angle translated into the second and third quadrants. go up 60 degrees from the negative side of the x axis, that is take 180 - 60, and you got 120 degrees. That's one solution. The other one is to go 60 degrees past 180, into the third quadrant, that is, 180 + 60 = 240 degrees, that's the other solution.

Now, if they'd asked for all possible solutions youd do the same thing but then you'd also say "plus 360n degrees", meaning, these positions with an arbitrary number of rotations added.

Answer 3

2 cos x + 1 = 0
2 cos x = -1 (transpose 1 to the other side of the equartion)
cos x = -1/2 (then divide both sides by 2)
arc cos x = 60 degrees (then type on calcu. shift cos -.5)

voila!!!that's the answer..

Answer 4

2 * (a million - cos(x)^2) - cos(x) - a million = 0 2 - 2cos(x)^2 - cos(x) - a million = 0 -2cos(x)^2 - cos(x) + a million = 0 2cos(x)^2 + cos(x) - a million = 0 cos(x) = (-a million +/- sqrt(a million + 8)) / 4 cos(x) = (-a million +/- 3) / 4 cos(x) = -4/4 , 2/4 cos(x) = -a million , a million/2 x = 60 , one hundred eighty , 3 hundred

Answer 5

I myself prefer working with radians, and then convert to degrees after.

2cos(x) + 1 = 0

To solve this, we must isolate cos(x).

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

And at this point, we ask ourselves: where on the graph is cos(x) equal to -1/2? This occurs in quadrants 2 and 3, and at the values 2pi/3 and 4pi/3.

Therefore, x = {2pi/3, 4pi/3}

And, converting those to degrees (we need to multiply 180/pi for the conversion to each term}

x = {120, 240}

Answer 6

2cosx=-1
cosx=-1/2
The cos of what angle = -1/2

Answer 7

2cosx=-1
cosx=-1/2
x is in thesecond or third quadrant
x=180-60 or 180 +60
=120* or 240*