Degrees vs Radians — What is a Radian | Trigonometry
Автор: Mathematika Labs EN
Загружено: 2026-02-05
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📐 Degrees vs Radians — What is a Radian (Visually Explained) | Trigonometry.
In this video, we explain the radian in a clear and visual way using the unit circle.
A radian is defined as the angle that subtends an arc whose length is exactly equal to the radius R of the circle.
By laying the radius along the circumference, we can see what “1 radian” really means.
Then we answer the key question:
✅ How many radians are there in a semicircle?
In other words, how many radians correspond to 180°?
By counting along the semicircle, we get:
1 radian
2 radians
3 radians
plus a small remaining part (about 0.141592…)
This leads to the famous result:
180° = 3.14… radians = π radians (an irrational number).
Finally, we summarize the main degree–radian conversions:
90° = π/2
180° = π
360° = 2π
🎯 Perfect for high school students, beginners in trigonometry, and anyone who wants to understand radians instead of memorizing formulas.
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