To solve the inequality cos x <= -0.5, we need to find the values of x that satisfy this condition.
First, we need to determine when cos x is less than or equal to -0.5. We know that the cosine function has a range of -1 to 1, and since -0.5 lies outside this range, we need to find the values of x where cos x reaches this limit.
To find these values, we can use the unit circle to determine when the cosine function is -0.5. At x = 2π/3 and x = 4π/3, cos x = -0.5.
Therefore, the solution to the inequality cos x <= -0.5 is x ∈ [2π/3 + 2πn, 4π/3 + 2πn], where n is an integer. This represents all values of x where cos x is less than or equal to -0.5.
To solve the inequality cos x <= -0.5, we need to find the values of x that satisfy this condition.
First, we need to determine when cos x is less than or equal to -0.5. We know that the cosine function has a range of -1 to 1, and since -0.5 lies outside this range, we need to find the values of x where cos x reaches this limit.
To find these values, we can use the unit circle to determine when the cosine function is -0.5. At x = 2π/3 and x = 4π/3, cos x = -0.5.
Therefore, the solution to the inequality cos x <= -0.5 is x ∈ [2π/3 + 2πn, 4π/3 + 2πn], where n is an integer. This represents all values of x where cos x is less than or equal to -0.5.