Small-angle approximation: Difference between revisions

Revision as of 00:17, 22 December 2023

Revision as of 05:03, 22 December 2023

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==== Dual numbers ====

By using the Maclaurin series of cosine and sine and substituting in θ=θε, where ε is the symbol used in dual numbers, often considered similar to an infinitesimal amount, with a square of 0, the result is that cos(θε)=1 and sin(θε)=θε. These approximations satisfy the Pythagorean Identity, as cos²(θε)+sin²(θε)=1²+(θε)²=1+θ²ε²=1+θ²0=1.

==Error of the approximations==