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Small-angle approximations

Everything is in radians.

Function
Approx: sinθ ≈ θ
Angle θ (radians)
0.3500.350
Actual vs approximation
x: radians (−π/2 → π/2) • y: −1 → 1
−π/2−π/3−π/60π/6π/3π/2-1.00-0.50000.5001.00θ (radians)y
θ
0.350 rad
Actual
0.343
Approx
0.350
Absolute error
0.00710
% error
2.07%
Unit Circle
1−11−1
sinθ
0.343
cosθ
0.939
tanθ
0.365

The point given by the pink circle is (0.939, 0.343). cosθ is the y-coordinate and sinθ is the x-coordinate.