Find all values of x in the interval [0, 2 pi] that satisfy 2 cos x-1 = 0.
cos x = 1/2
x = 60
How do I find the other value of x?
cosX= 1/2
x= 60, x= 60+180 degrees.
To find the other value of x, we need to consider the properties of the cosine function. The cosine function has a periodicity of 2π, meaning that it repeats every 2π radians.
In this case, we know that cos(x) = 1/2. Using the unit circle or reference angles, we can determine that one solution is x = π/3 (or 60 degrees in degrees).
To find the second solution, we add the period of 2π to the first solution. So we add 2π radians to π/3:
x = π/3 + 2π
Simplifying this expression, we get:
x = π/3 + 6π/3
x = 7π/3
Therefore, the two values of x that satisfy the equation 2cos(x) - 1 = 0 in the interval [0, 2π] are x = π/3 and x = 7π/3.