"cos" ⁡〖"α" ="1" /"2" 〗

1 answer

There are actually many values of alpha (α) such that cos⁡(α) = 1/2. Here are a few examples:

- α = 60 degrees (or π/3 radians). In a 30-60-90 right triangle, the adjacent side (which is half the length of the hypotenuse) has a ratio of 1/2 to the hypotenuse, so cos⁡(60) = 1/2.
- α = 300 degrees (or 5π/3 radians). This is simply the negative angle of α = 60 degrees, since cosine is an even function (i.e. cos⁡(-x) = cos⁡(x)).
- α = π/3 - 2πn or 5π/3 + 2πn, where n is any integer. These are all angles that are coterminal with α = 60 degrees, since adding or subtracting a full revolution (2π radians) doesn't change the value of cosine.