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10 cards from this deck
sinθ≈θ\sin \theta \approx \thetasinθ≈θ
cosθ≈1−θ2/2\cos \theta \approx 1 - \theta^2/2cosθ≈1−θ2/2
tanθ≈θ\tan \theta \approx \thetatanθ≈θ
sinθ\sin \thetasinθ approaches θ\thetaθ as θ\thetaθ approaches 000.
Taylor series expansions around θ=0\theta = 0θ=0.
In physics, engineering, and calculus.
sin(0.1)≈0.1\sin(0.1) \approx 0.1sin(0.1)≈0.1
cos(0.05)≈0.99875\cos(0.05) \approx 0.99875cos(0.05)≈0.99875
limθ→0sinθθ=1\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1limθ→0θsinθ=1
They simplify calculations involving small angles.
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