Small Angle Approximations (AQA A-Level Mathematics): Quizzes

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Small Angle Approximations
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For small θ\theta in radians, what is the approximation for sinθ\sin \theta?

sinθθ\sin \theta \approx \theta

For small θ\theta in radians, what is the approximation for cosθ\cos \theta?

cosθ1θ22\cos \theta \approx 1 - \frac{\theta^2}{2}

For small θ\theta in radians, what is the approximation for tanθ\tan \theta?

tanθθ\tan \theta \approx \theta

In which units must θ\theta be measured for small angle approximations to work?

Radians

What is the first term in the Taylor series expansion of sinθ\sin \theta around θ=0\theta = 0?

θ\theta

What is the first term in the Taylor series expansion of cosθ\cos \theta around θ=0\theta = 0?

11

In which field are small angle approximations used for pendulum motion analysis?

Physics

Using small angle approximations, what does sin4θ3θ\frac{\sin 4\theta}{3\theta} simplify to for small θ\theta?

43\frac{4}{3}

When θ\theta is small, which terms can be neglected as insignificantly small?

θ3\theta^3 and above

Using small angle approximations, what is limθ0sinθθ\lim_{\theta \to 0} \frac{\sin \theta}{\theta}?

11

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