Find area of region R

Question

Region $R$ contains all the points $(x,y)$ such that $x^2+y^2 \le 100$ and $ \sin (x+y) \ge 0$. Find the area of region $R$.

I can't seem to proceed except for the fact that the inequalities give that $x$ and $y$ do not exceed $10$ and their sum isn't a multiple of $π$

Help would be appreciated. There was an answer provided earlier(on StackExchange), but I couldn't understand much from it and would like an explicit solution.

Thanks again.

Answer 1

Now you can figure out what the regions will be (@achille hui's hint.)