Answer
negative
Work Step by Step
RECALL:
The quadrantal angles are:
Positive x-axis: $0$ radians;
Positive y-axis: $\frac{3.14}{2} = 1.57$ radians;
Negative x-axis: $3.14$ radians;
Negative y-axis: $4.61$ radians
Positive x-axis: $6,18$ radians
Thus, when moving counterclockwise from the positive x-axis, the angle $2$ radians is beyond the positive y-axis but before the negative x-axis.
This means that the angle is in Quadrant II.
With $\cos{\theta}=x$, and since the value of $x$ is negative in Quadrant II, then $\cos{2}$ must be negative.
