12. Maximum 15 points. Let $[x]$ denote the integer part of the number $x$ (i.e., the greatest integer not exceeding $x$).

Solve the equation.

$$
[\sin x+\cos x]=1
$$

#
# Solution:

The given equation is equivalent to the double inequality

$$
1 \leq \sin x + \cos x \text{ correct answer } | 15 |
| The algorithm is provided, but one of the transitions is not justified, correct answer obtained | 10 |
| The algorithm is provided, correct answer obtained only for one trigonometric circle starting at zero and ending at 2pi | 5 |
| The solution does not meet any of the presented criteria | 0 |