Understanding the Cosine Function | Evaluating cos(2π) and its Value

Cos(2π)

The cosine function, denoted as cos(x), is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle

The cosine function, denoted as cos(x), is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle. It is a periodic function, meaning it repeats itself after a certain interval. In this case, we are evaluating the cosine of 2π.

First, let’s understand what 2π represents. In radians, 2π is equivalent to one complete revolution around a circle. One full revolution represents a 360-degree angle. Since cosine is also a periodic function with a period of 2π, cos(2π) will have the same value as cos(0), cos(2π), or any value of the form n * 2π, where n is an integer.

Using the unit circle, we can determine the value of cos(2π). On the unit circle, the x-coordinate of a point on the circumference represents the cosine of the corresponding angle.

At 2π radians or 360 degrees, we return to the starting point on the unit circle, which is (1, 0). Therefore, cos(2π) is equal to the x-coordinate of this point, which is simply 1.

Therefore, cos(2π) = 1.

In summary, the cosine of 2π is equal to 1.

More Answers: