Question

what is the value of the following trig. function? (unit circle) cos 2π -1 0 180 1

Explanation:

Step1: Recall unit - circle definition

On the unit circle, for an angle $\theta$, the cosine function is defined as the $x$ - coordinate of the point where the terminal side of the angle intersects the unit circle.

Step2: Identify the angle position

The angle $\theta = 2\pi$ radians corresponds to a full - revolution around the unit circle. The terminal side of the angle $\theta = 2\pi$ coincides with the positive $x$ - axis.

Step3: Determine the cosine value

The point on the unit circle where the terminal side of the angle $\theta = 2\pi$ intersects is $(1,0)$. Since $\cos\theta$ is the $x$ - coordinate of this point, $\cos(2\pi)=1$.

Answer:

D. 1