Answer
$\sin{2} \gt \cos{2}$
Work Step by Step
RECALL:
(1) The sine function is increasing in the interval $(0, \frac{\pi}{2})$ or $(0, 1.57)$ and decreasing in the interval $(\frac{\pi}{2}, \pi)$ or $(1.57, 3.14)$
This means that from the angle $0$ radians to $1.57$ radians, the value of the sine function increases from $0$ to $1$, while from the angle $1.57$ radians to $3.14$ radians, the value of the sine function is decreasing from $1$ to $0$.
(2) The cosine function is decreasing in the interval $(0, 3.14)$, and $\cos{1.57}=0$. This means that from the angle $1.57$ radians to $3.14$ radians, the value of the cosine function approaches $-1$
Thus,
$\sin{2}$ is positive while $\cos{2}$ is negative.
Therefore, $\sin{2} \gt \cos{2}$.
