Maths for Electronics L13: Radians — why 360° = 2π
One radian is the angle where the arc equals the radius (≈ 57.3°), a full turn is 2π radians, which is why AC formulas use 2πf.
Why is a full circle 2π? 🔄 Radians in 20 seconds 👇
1️⃣ ONE RADIAN: take the radius and bend it around the edge of the circle. The angle it covers is 1 radian ≈ 57.3°.
2️⃣ A FULL TURN: about 6.28 radii fit all the way round (the circumference is 2π × r). So 360° = 2π radians, 180° = π and 90° = π/2.
3️⃣ WHY ELECTRONICS CARES: AC maths uses ω = 2πf. A 50 Hz supply turns 2π × 50 ≈ 314 radians every second (60 Hz in the USA → ≈ 377 rad/s). That's the 2πf you see in sin(2πft) and in every AC formula.
One radian = one radius of arc!
Read the voiceover (transcript)
- Why is a full circle two pi?
- Bend the radius around the edge. That angle is one radian, about fifty-seven degrees!
- A full turn fits two pi radii, about six point two eight. So three sixty degrees is two pi!
- That's why AC uses two pi f. Fifty hertz turns three hundred fourteen radians a second!
- One radian, one radius!
- Next: efficiency! Follow for lesson fourteen!
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