Angles can be measured in degrees, radians, or gradians. Degrees are intuitive, radians are essential for math, gradians simplify right angles.
Degrees
A degree divides a circle into 360 parts. 1° = 60' (arcminutes) = 3,600" (arcseconds). Dates back to Babylonian base-60 math.
Radians
1 radian = arc length equal to radius. Full circle = 2π rad ≈ 6.2832. Radians are essential for calculus: d/dx(sin x) = cos x only in radians.
Conversions
- 360° = 2π rad = 400 grad
- 1° = π/180 rad ≈ 0.01745 rad
- 1 rad ≈ 57.296°
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Frequently Asked Questions
How do I convert degrees to radians?
Multiply by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 rad.
Why do mathematicians prefer radians?
Radians simplify calculus. The derivative of sin(x) = cos(x) only in radians. Taylor series also require radians.