Trigonometric derivatives are fundamental in both mathematics and physics, yet their correct application, particularly the distinction between radians and degrees, remains a significant challenge for college students worldwide. This study identifies a widespread "blind spot" in understanding trigonometric derivatives and their implications for physical systems, highlighting a critical gap in physics education. A multinational survey of 769 college students, primarily undergraduate and graduate science, technology, engineering, and mathematics (majors, from Israel, the United States, China, and India assessed their ability to differentiate between radians and degrees in mathematical and physical contexts, focusing on harmonic motion. Results reveal that only 26.3% of students correctly identified that the well-known expressions for trigonometric derivatives hold exclusively in radians, while 70.7% incorrectly assumed that both radians and degrees are valid. Notably, students demonstrated improved recognition of radians in physical contexts (59% correct responses) compared to mathematical ones, suggesting that students rely on familiar physical equations as cognitive reference points when applying mathematical concepts. These misunderstandings appear globally, suggesting a universal challenge. The findings highlight the need for curriculum reforms to better connect mathematical formalism with physical application.