Mathematics 2000 JAMB Past Questions - Question 23: Find the minimum value of the function f(0)=2/3-Cos 0 for 0 ≤ 0 ≤ 2π

Correct Answer

B

Explanation

To find the minimum value of the function f(θ) = 2/3 - cos(θ) for 0 ≤ θ ≤ 2π, we can analyze the behavior of the cosine function within this interval.The cosine function oscillates between -1 and 1. Since we are subtracting the cosine function from 2/3, the maximum value of the function occurs when the cosine function is at its minimum value of -1. Similarly, the minimum value of the function occurs when the cosine function is at its maximum value of 1.Therefore, the minimum value of f(θ) = 2/3 - cos(θ) is obtained when cos(θ) = 1. This occurs when θ = 0.Substituting θ = 0 into the function, we have:f(0) = 2/3 - cos(0)f(0) = 2/3 - 1f(0) = 2/3 - 3/3f(0) = -1/3Hence, the minimum value of the function f(θ) = 2/3 - cos(θ) for 0 ≤ θ ≤ 2π is -1/3.