Ah, beta, radians are the natural measure because they connect the angle directly to the arc length on a unit circle! When x is tiny, sin x is almost the vertical line, and x is the tiny curved arc… in radians, those lengths are *equal*, so ratio is 1. In degrees? You're comparing apples and oranges with a conversion factor! 📐
It’s like my chana masala recipe: if you use "katori" for dal and "cup" for water, the proportion is perfect. But if you switch one to "litre" mid-way? Disaster! The math must use matching, natural units to get that perfect, satisfying "whistle" of a correct answer. Maza aa gaya samjha? 😄
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