beautiful
姚 centers on beauty, especially in a feminine or graceful sense. The given meaning 'beautiful' is the core idea.
姚 combines 女 (woman) with 兆, which likely contributes the sound. The character is associated with beauty, possibly through the idea of a beautiful woman.
A woman (女) beside the sign 兆: imagine a woman whose beauty is as striking as a good omen (兆 can suggest an omen or sign).
For ヨウ, picture a beautiful woman saying 'yo!' to get attention: yo -> ヨウ, and her beauty makes everyone turn.