Pure · Trigonometry
Chapter 1 · 3
The idea
Small angle approximations
The radian approximations sin θ ≈ θ, tan θ ≈ θ and cos θ ≈ 1 − ½θ², why they hold, and using them to approximate expressions and evaluate limiting ratios for small θ.
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Pure · Trigonometry
Small angle approximations
The radian approximations sin θ ≈ θ, tan θ ≈ θ and cos θ ≈ 1 − ½θ², why they hold, and using them to approximate expressions and evaluate limiting ratios for small θ.
Why it works
The three approximations
Trig functions are hard to do algebra on; polynomials are easy. The payoff of this topic is that near zero, trig functions ARE polynomials, near enough — which is what makes limiting ratios (and later, differentiating from first principles) possible. When is small and measured in radians:Keep reading — free
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