cos a = 1/2 for all 0 ≤ α ≤ 2π
This statement is false.
When α = 0 or 2π, cos α = cos 0 = 1, not 1/2.
When α = π, cos α = cos π = -1, not 1/2.
Therefore, there are three values of α where cos α is not equal to 1/2, and the statement is false.
To solve for α when cos α = 1/2 for all 0 ≤ α ≤ 2π, we can use the inverse cosine function. The inverse cosine function is denoted as acos(x).
Step 1: Start with the given equation cos α = 1/2.
Step 2: Take the inverse cosine of both sides: α = acos(1/2).
Step 3: Use the unit circle or a calculator to find the values of α that satisfy the equation.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) in a coordinate plane. With this information, we can find the values of α for which cos α = 1/2.
On the unit circle, the x-coordinate corresponds to the cosine value. The x-coordinate of the point on the unit circle where cos α = 1/2 is √3/2.
Therefore, acos(1/2) = α = π/3 and 5π/3, since these are the two angles where cos α = 1/2 on the unit circle within the range 0 ≤ α ≤ 2π.
So, the solution is α = π/3 and 5π/3 when cos α = 1/2 for all 0 ≤ α ≤ 2π.