Small-angle Approximation - Error of The Approximations

Error of The Approximations

Figure 3 shows the relative errors of the small angle approximations. The angles at which the relative error exceeds 1% are as follows:

• tan θ ≈ θ at about 0.176 radians.
• sin θ ≈ θ at about 0.244 radians.
• cos θ ≈ 1 - θ2/2 at about 0.664 radians.