Radian measure of an angle
A central angle subtending an arc equal in length to the radius is called 1 radian (1 rad). Since a semicircle has length πR, 180° = π rad, so 1 rad = 180° : π ≈ 57.3°. Conversion formulas: α rad = (180 · α : π)°; α° = (π · α : 180) rad. Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π. When an angle is given in radians the word “rad” is usually omitted. On a circle of radius R, an angle of α radians subtends an arc of length l = αR; a sector with radius R and angle α has area S = R²α : 2. On a circle of radius 1 the arc length equals the radian measure of the angle.
“Angle dominoes”: cards have degrees (30°, 45°, 60°, 90°, 120°, 180°) on one half and radians (π/6, π/4, ...) on the other; students join the correct pairs.