arcsin1

We are asked to compute -arcsin(-1) * 0.2 (in radians) and take the digits between positions 10000 and 10099 of the decimal part of the result.

First of all, let’s do the math:

$$ \sin{\left(\frac{-\pi}{2}\right)} = -1 \iff \arcsin{(-1)} = \frac{-\pi}{2} $$

Notice that the inverse sine function is bounded: $\frac{-\pi}{2} \leq \arcsin{x} \leq \frac{\pi}{2}$ for $x \in \mathbb{R}$. Therefore:

$$ -\arcsin{(-1)} \cdot 0.2 = - \left(\frac{-\pi}{2}\right) \cdot 0.2 = \frac{\pi}{10} $$

So we are asked for the 10000th-10099th digits of $\pi$. We are given a sanity check:

in case I messed up - first digit is 7, last digit is 2, 100 digits total

So the flag is:

ictf{7856672279661988578279484885583439751874454551296563443480396642055798293680435220277098429423253302}