Solve the equation 2cos(x)+1=0
, 0≤x≤2π
. Show all of your work.
To solve the equation 2cos(x) + 1 = 0, first subtract 1 from both sides:
2cos(x) = -1
Then divide by 2:
cos(x) = -1/2
To find the values of x that satisfy this equation within the interval 0 ≤ x ≤ 2π, we can look at the unit circle or use the reference angle of π/3.
In the unit circle, the cosine value is -1/2 in the second and third quadrants. This occurs at angles π/3 and 5π/3.
Therefore, the solutions to the equation within the interval 0 ≤ x ≤ 2π are x = π/3 and x = 5π/3.