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

📚Quizzes
Small Angle Approximations
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

For small θ\theta in radians, what is the approximation for sin⁡θ\sin \theta?

sin⁡θ≈θ\sin \theta \approx \theta

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

cos⁡θ≈1−θ22\cos \theta \approx 1 - \frac{\theta^2}{2}

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

tan⁡θ≈θ\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 sin⁡θ\sin \theta around θ=0\theta = 0?

θ\theta

What is the first term in the Taylor series expansion of cos⁡θ\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 sin⁡4θ3θ\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 lim⁡θ→0sin⁡θθ\lim_{\theta \to 0} \frac{\sin \theta}{\theta}?

11

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.