Question

find the exact value of $\cos 2\pi$.
$\cos 2\pi = \square$

Explanation:

Step1: Recall the unit circle definition

The cosine of an angle in the unit circle is the x - coordinate of the point on the unit circle corresponding to that angle. For an angle of \(2\pi\) radians, the point on the unit circle is \((1,0)\) because \(2\pi\) radians is a full rotation (equivalent to \(360^{\circ}\)) and the starting point (and the point after a full rotation) on the unit circle is \((1,0)\).

Step2: Determine the value of \(\cos(2\pi)\)

Since \(\cos(\theta)\) is the x - coordinate of the point \((x,y)\) on the unit circle for angle \(\theta\), and for \(\theta = 2\pi\), the x - coordinate is 1, we have \(\cos(2\pi)=1\).

Answer:

\(1\)